4(4x^2-72x-75)=0

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Solution for 4(4x^2-72x-75)=0 equation:


Simplifying
4(4x2 + -72x + -75) = 0

Reorder the terms:
4(-75 + -72x + 4x2) = 0
(-75 * 4 + -72x * 4 + 4x2 * 4) = 0
(-300 + -288x + 16x2) = 0

Solving
-300 + -288x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-75 + -72x + 4x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-75 + -72x + 4x2)' equal to zero and attempt to solve: Simplifying -75 + -72x + 4x2 = 0 Solving -75 + -72x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -18.75 + -18x + x2 = 0 Move the constant term to the right: Add '18.75' to each side of the equation. -18.75 + -18x + 18.75 + x2 = 0 + 18.75 Reorder the terms: -18.75 + 18.75 + -18x + x2 = 0 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + -18x + x2 = 0 + 18.75 -18x + x2 = 0 + 18.75 Combine like terms: 0 + 18.75 = 18.75 -18x + x2 = 18.75 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = 18.75 + 81 Reorder the terms: 81 + -18x + x2 = 18.75 + 81 Combine like terms: 18.75 + 81 = 99.75 81 + -18x + x2 = 99.75 Factor a perfect square on the left side: (x + -9)(x + -9) = 99.75 Calculate the square root of the right side: 9.987492178 Break this problem into two subproblems by setting (x + -9) equal to 9.987492178 and -9.987492178.

Subproblem 1

x + -9 = 9.987492178 Simplifying x + -9 = 9.987492178 Reorder the terms: -9 + x = 9.987492178 Solving -9 + x = 9.987492178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 9.987492178 + 9 Combine like terms: -9 + 9 = 0 0 + x = 9.987492178 + 9 x = 9.987492178 + 9 Combine like terms: 9.987492178 + 9 = 18.987492178 x = 18.987492178 Simplifying x = 18.987492178

Subproblem 2

x + -9 = -9.987492178 Simplifying x + -9 = -9.987492178 Reorder the terms: -9 + x = -9.987492178 Solving -9 + x = -9.987492178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -9.987492178 + 9 Combine like terms: -9 + 9 = 0 0 + x = -9.987492178 + 9 x = -9.987492178 + 9 Combine like terms: -9.987492178 + 9 = -0.987492178 x = -0.987492178 Simplifying x = -0.987492178

Solution

The solution to the problem is based on the solutions from the subproblems. x = {18.987492178, -0.987492178}

Solution

x = {18.987492178, -0.987492178}

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