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Simplifying 4x2 + -90x + -576 = 0 Reorder the terms: -576 + -90x + 4x2 = 0 Solving -576 + -90x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-288 + -45x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-288 + -45x + 2x2)' equal to zero and attempt to solve: Simplifying -288 + -45x + 2x2 = 0 Solving -288 + -45x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -144 + -22.5x + x2 = 0 Move the constant term to the right: Add '144' to each side of the equation. -144 + -22.5x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + -22.5x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + -22.5x + x2 = 0 + 144 -22.5x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 -22.5x + x2 = 144 The x term is -22.5x. Take half its coefficient (-11.25). Square it (126.5625) and add it to both sides. Add '126.5625' to each side of the equation. -22.5x + 126.5625 + x2 = 144 + 126.5625 Reorder the terms: 126.5625 + -22.5x + x2 = 144 + 126.5625 Combine like terms: 144 + 126.5625 = 270.5625 126.5625 + -22.5x + x2 = 270.5625 Factor a perfect square on the left side: (x + -11.25)(x + -11.25) = 270.5625 Calculate the square root of the right side: 16.44878415 Break this problem into two subproblems by setting (x + -11.25) equal to 16.44878415 and -16.44878415.Subproblem 1
x + -11.25 = 16.44878415 Simplifying x + -11.25 = 16.44878415 Reorder the terms: -11.25 + x = 16.44878415 Solving -11.25 + x = 16.44878415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.25' to each side of the equation. -11.25 + 11.25 + x = 16.44878415 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = 16.44878415 + 11.25 x = 16.44878415 + 11.25 Combine like terms: 16.44878415 + 11.25 = 27.69878415 x = 27.69878415 Simplifying x = 27.69878415Subproblem 2
x + -11.25 = -16.44878415 Simplifying x + -11.25 = -16.44878415 Reorder the terms: -11.25 + x = -16.44878415 Solving -11.25 + x = -16.44878415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.25' to each side of the equation. -11.25 + 11.25 + x = -16.44878415 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = -16.44878415 + 11.25 x = -16.44878415 + 11.25 Combine like terms: -16.44878415 + 11.25 = -5.19878415 x = -5.19878415 Simplifying x = -5.19878415Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.69878415, -5.19878415}Solution
x = {27.69878415, -5.19878415}
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