Final answer:
To solve the quadratic equation x²+2x=8, we factor it to (x + 4)(x - 2) = 0 and get the solutions x = -4 and x = 2. While the quadratic formula could also be used, factoring proves to be simpler in this case.
Step-by-step explanation:
To find the value of x in the equation x²+2x=8, we want to rearrange the equation into a standard quadratic form, which is ax² + bx + c = 0. First, we subtract 8 from both sides to obtain x² + 2x - 8 = 0. This is a quadratic equation that can be solved by factoring, completing the square, or using the quadratic formula.
To solve by factoring, we would look for two numbers that multiply to -8 and add to 2 (the coefficient of x). These numbers are +4 and -2, so we can express the quadratic as (x + 4)(x - 2) = 0. Setting each factor equal to zero gives us the solutions x = -4 or x = 2.
If we were to complete the square, we'd want to form a perfect square trinomial on the left side of the equation. However, in this case, factoring is more straightforward.
Using the quadratic formula, which is x = (-b ± √(b²-4ac))/(2a), where a = 1, b = 2, and c = -8, we'd calculate the determinant (√(2² - 4(1)(-8))) and then find the two possible values for x. However, factoring is the easier route here.