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Simplifying -4x2 + 160x + -270 = 0 Reorder the terms: -270 + 160x + -4x2 = 0 Solving -270 + 160x + -4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-135 + 80x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-135 + 80x + -2x2)' equal to zero and attempt to solve: Simplifying -135 + 80x + -2x2 = 0 Solving -135 + 80x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 67.5 + -40x + x2 = 0 Move the constant term to the right: Add '-67.5' to each side of the equation. 67.5 + -40x + -67.5 + x2 = 0 + -67.5 Reorder the terms: 67.5 + -67.5 + -40x + x2 = 0 + -67.5 Combine like terms: 67.5 + -67.5 = 0.0 0.0 + -40x + x2 = 0 + -67.5 -40x + x2 = 0 + -67.5 Combine like terms: 0 + -67.5 = -67.5 -40x + x2 = -67.5 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -67.5 + 400 Reorder the terms: 400 + -40x + x2 = -67.5 + 400 Combine like terms: -67.5 + 400 = 332.5 400 + -40x + x2 = 332.5 Factor a perfect square on the left side: (x + -20)(x + -20) = 332.5 Calculate the square root of the right side: 18.234582529 Break this problem into two subproblems by setting (x + -20) equal to 18.234582529 and -18.234582529.Subproblem 1
x + -20 = 18.234582529 Simplifying x + -20 = 18.234582529 Reorder the terms: -20 + x = 18.234582529 Solving -20 + x = 18.234582529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 18.234582529 + 20 Combine like terms: -20 + 20 = 0 0 + x = 18.234582529 + 20 x = 18.234582529 + 20 Combine like terms: 18.234582529 + 20 = 38.234582529 x = 38.234582529 Simplifying x = 38.234582529Subproblem 2
x + -20 = -18.234582529 Simplifying x + -20 = -18.234582529 Reorder the terms: -20 + x = -18.234582529 Solving -20 + x = -18.234582529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -18.234582529 + 20 Combine like terms: -20 + 20 = 0 0 + x = -18.234582529 + 20 x = -18.234582529 + 20 Combine like terms: -18.234582529 + 20 = 1.765417471 x = 1.765417471 Simplifying x = 1.765417471Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.234582529, 1.765417471}Solution
x = {38.234582529, 1.765417471}
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