Problem

$4 x^{2}+32 x-36=0$

Answer

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Answer

Final Answer: The solutions to the equation \(4 x^{2}+32 x-36=0\) are \(\boxed{-9.0}\) and \(\boxed{1.0}\)

Steps

Step 1 ：Given the quadratic equation \(4 x^{2}+32 x-36=0\)

Step 2 ：This is a quadratic equation of the form \(ax^{2} + bx + c = 0\). The solutions to this equation can be found using the quadratic formula \(x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}\)

Step 3 ：Here, a = 4, b = 32, c = -36

Step 4 ：Calculate the discriminant D = \(b^{2} - 4ac = 1600\)

Step 5 ：Substitute a, b, and D into the quadratic formula to find the solutions

Step 6 ：The solutions are \(x1 = -9.0\) and \(x2 = 1.0\)

Step 7 ：Final Answer: The solutions to the equation \(4 x^{2}+32 x-36=0\) are \(\boxed{-9.0}\) and \(\boxed{1.0}\)

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