Algebra

To solve the quadratic equation x^2 - 2x - 3 = 0, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. In this case, a = 1, b = -2, and c = -3. Plugging these values into the formula, we get x = (-(-2) ± √((-2)^2 - 4(1)(-3))) / 2(1). Simplifying this expression, we get x = (2 ± √(4 + 12)) / 2. Further simplifying, we get x = (2 ± √16) / 2. Finally, we get x = (2 ± 4) / 2. This gives us two solutions: x = 1 and x = -3.

To solve the equation 8x + 5 = 21, we need to isolate the variable x on one side of the equation. We can do this by subtracting 5 from both sides of the equation, which gives us 8x = 16. Then, we can divide both sides of the equation by 8, which gives us x = 2.

To solve the equation 9x - 6 = 15, we need to isolate the variable x on one side of the equation. We can do this by adding 6 to both sides of the equation, which gives us 9x = 21. Then, we can divide both sides of the equation by 9, which gives us x = 3.

To solve the equation, we need to isolate the variable x on one side of the equation. First, we subtract 5 from both sides: 3x + 5 - 5 = 17 - 5, which simplifies to 3x = 12. Then, we divide both sides by 3: 3x / 3 = 12 / 3, which gives us x = 4.

To solve the equation, we first distribute the 2 to the terms inside the parentheses: 2x - 6 = 10. Then, we add 6 to both sides: 2x - 6 + 6 = 10 + 6, which simplifies to 2x = 16. Finally, we divide both sides by 2: 2x / 2 = 16 / 2, which gives us x = 8.

To solve the equation, we first get all the terms with x on one side of the equation and all the constant terms on the other side. We can do this by subtracting 3x from both sides: 3x - 2 - 3x = 5x + 4 - 3x, which simplifies to -2 = 2x + 4. Then, we subtract 4 from both sides: -2 - 4 = 2x + 4 - 4, which gives us -6 = 2x. Finally, we divide both sides by 2: -6 / 2 = 2x / 2, which gives us x = -3.

To solve the equation, we first get all the terms with x on one side of the equation and all the constant terms on the other side. We can do this by subtracting 2x from both sides: 2x + 3 - 2x = 4x - 5 - 2x, which simplifies to 3 = 2x - 5. Then, we add 5 to both sides: 3 + 5 = 2x - 5 + 5, which gives us 8 = 2x. Finally, we divide both sides by 2: 8 / 2 = 2x / 2, which gives us x = 4.

To solve the equation, we first distribute the 5 and 3 to the terms inside the parentheses: 5x + 10 = 3x - 12. Then, we get all the terms with x on one side of the equation and all the constant terms on the other side: 5x - 3x = -12 - 10, which simplifies to 2x = -22. Finally, we divide both sides by 2: 2x / 2 = -22 / 2, which gives us x = -11.

To solve the equation, we first distribute the 2 and 4 to the terms inside the parentheses: 6x - 2 = 4x + 8. Then, we get all the terms with x on one side of the equation and all the constant terms on the other side: 6x - 4x = 8 + 2, which simplifies to 2x = 10. Finally, we divide both sides by 2: 2x / 2 = 10 / 2, which gives us x = 5.

To solve the equation, we first get all the terms with x on one side of the equation and all the constant terms on the other side. We can do this by subtracting 2x from both sides: 3x + 5 - 2x = 2x - 7 - 2x, which simplifies to x + 5 = -7. Then, we subtract 5 from both sides: x + 5 - 5 = -7 - 5, which gives us x = -12.

To solve the equation, we first distribute the 4 and 2 to the terms inside the parentheses: 4x - 12 = 2x + 10. Then, we get all the terms with x on one side of the equation and all the constant terms on the other side: 4x - 2x = 10 + 12, which simplifies to 2x = 22. Finally, we divide both sides by 2: 2x / 2 = 22 / 2, which gives us x = 11.

To solve the equation, we first get all the terms with x on one side of the equation and all the constant terms on the other side. We can do this by subtracting 3x from both sides: 5x - 2 - 3x = 3x + 8 - 3x, which simplifies to 2x - 2 = 8. Then, we add 2 to both sides: 2x - 2 + 2 = 8 + 2, which gives us 2x = 10. Finally, we divide both sides by 2: 2x / 2 = 10 / 2, which gives us x = 5.

To solve the equation, we first distribute the 2 and 4 to the terms inside the parentheses: 2x + 6 = 4x - 4. Then, we get all the terms with x on one side of the equation and all the constant terms on the other side: 2x - 4x = -4 - 6, which simplifies to -2x = -10. Finally, we divide both sides by -2: -2x / -2 = -10 / -2, which gives us x = 5.

To solve the equation, we first distribute the 3 and 2 to the terms inside the parentheses: 3x - 6 = 2x + 8. Then, we get all the terms with x on one side of the equation and all the constant terms on the other side: 3x - 2x = 8 + 6, which simplifies to x = 14. Finally, we check our answer by substituting x = 14 back into the original equation: 3(14 - 2) = 2(14 + 4), which simplifies to 3(12) = 2(18), which is true.

To solve the equation, we first distribute the 5 and 3 to the terms inside the parentheses: 5x - 5 = 6x + 12. Then, we get all the terms with x on one side of the equation and all the constant terms on the other side: 5x - 6x = 12 + 5, which simplifies to -x = 17. Finally, we multiply both sides by -1 to isolate x: -x * -1 = 17 * -1, which gives us x = -17.