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Simplifying 4x2 + -38x + 88 = 140 Reorder the terms: 88 + -38x + 4x2 = 140 Solving 88 + -38x + 4x2 = 140 Solving for variable 'x'. Reorder the terms: 88 + -140 + -38x + 4x2 = 140 + -140 Combine like terms: 88 + -140 = -52 -52 + -38x + 4x2 = 140 + -140 Combine like terms: 140 + -140 = 0 -52 + -38x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-26 + -19x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-26 + -19x + 2x2)' equal to zero and attempt to solve: Simplifying -26 + -19x + 2x2 = 0 Solving -26 + -19x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -13 + -9.5x + x2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + -9.5x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + -9.5x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -9.5x + x2 = 0 + 13 -9.5x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 -9.5x + x2 = 13 The x term is -9.5x. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5x + 22.5625 + x2 = 13 + 22.5625 Reorder the terms: 22.5625 + -9.5x + x2 = 13 + 22.5625 Combine like terms: 13 + 22.5625 = 35.5625 22.5625 + -9.5x + x2 = 35.5625 Factor a perfect square on the left side: (x + -4.75)(x + -4.75) = 35.5625 Calculate the square root of the right side: 5.963430221 Break this problem into two subproblems by setting (x + -4.75) equal to 5.963430221 and -5.963430221.Subproblem 1
x + -4.75 = 5.963430221 Simplifying x + -4.75 = 5.963430221 Reorder the terms: -4.75 + x = 5.963430221 Solving -4.75 + x = 5.963430221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = 5.963430221 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 5.963430221 + 4.75 x = 5.963430221 + 4.75 Combine like terms: 5.963430221 + 4.75 = 10.713430221 x = 10.713430221 Simplifying x = 10.713430221Subproblem 2
x + -4.75 = -5.963430221 Simplifying x + -4.75 = -5.963430221 Reorder the terms: -4.75 + x = -5.963430221 Solving -4.75 + x = -5.963430221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = -5.963430221 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -5.963430221 + 4.75 x = -5.963430221 + 4.75 Combine like terms: -5.963430221 + 4.75 = -1.213430221 x = -1.213430221 Simplifying x = -1.213430221Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.713430221, -1.213430221}Solution
x = {10.713430221, -1.213430221}
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