Final answer:
To solve the quadratic equation −10x²−12x = 5, we set it to zero and apply the quadratic formula with a = −10, b = −12, and c = 5, leading to two possible solutions for x after simplifying.
Step-by-step explanation:
To solve the quadratic equation −10x²−12x = 5, we will use the quadratic formula. First, we have to rearrange the equation by subtracting 5 from both sides to set the equation equal to zero, giving us −10x²−12x−5 = 0.
Next, we use the quadratic formula x = −b ± √(b² −4ac) / (2a), where a, b, and c are coefficients from the equation ax² + bx + c = 0. In this case, a = −10, b = −12, and c = 5. After substituting the values into the formula, we will find the two possible solutions for x.
To carry out the calculation, compute the discriminant √b² −4ac which is √((−12)² −4(−10)(5)) = √(144 + 200) = √344. Next, calculate the two possible values for x, x = (−12 ± √344) / (−20). Simplify by dividing by −4, which gives us x = (3 ± √86) / 5.