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Simplifying 4x2 + -124x + 468 = 0 Reorder the terms: 468 + -124x + 4x2 = 0 Solving 468 + -124x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(117 + -31x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(117 + -31x + x2)' equal to zero and attempt to solve: Simplifying 117 + -31x + x2 = 0 Solving 117 + -31x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-117' to each side of the equation. 117 + -31x + -117 + x2 = 0 + -117 Reorder the terms: 117 + -117 + -31x + x2 = 0 + -117 Combine like terms: 117 + -117 = 0 0 + -31x + x2 = 0 + -117 -31x + x2 = 0 + -117 Combine like terms: 0 + -117 = -117 -31x + x2 = -117 The x term is -31x. Take half its coefficient (-15.5). Square it (240.25) and add it to both sides. Add '240.25' to each side of the equation. -31x + 240.25 + x2 = -117 + 240.25 Reorder the terms: 240.25 + -31x + x2 = -117 + 240.25 Combine like terms: -117 + 240.25 = 123.25 240.25 + -31x + x2 = 123.25 Factor a perfect square on the left side: (x + -15.5)(x + -15.5) = 123.25 Calculate the square root of the right side: 11.101801656 Break this problem into two subproblems by setting (x + -15.5) equal to 11.101801656 and -11.101801656.Subproblem 1
x + -15.5 = 11.101801656 Simplifying x + -15.5 = 11.101801656 Reorder the terms: -15.5 + x = 11.101801656 Solving -15.5 + x = 11.101801656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + x = 11.101801656 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + x = 11.101801656 + 15.5 x = 11.101801656 + 15.5 Combine like terms: 11.101801656 + 15.5 = 26.601801656 x = 26.601801656 Simplifying x = 26.601801656Subproblem 2
x + -15.5 = -11.101801656 Simplifying x + -15.5 = -11.101801656 Reorder the terms: -15.5 + x = -11.101801656 Solving -15.5 + x = -11.101801656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + x = -11.101801656 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + x = -11.101801656 + 15.5 x = -11.101801656 + 15.5 Combine like terms: -11.101801656 + 15.5 = 4.398198344 x = 4.398198344 Simplifying x = 4.398198344Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.601801656, 4.398198344}Solution
x = {26.601801656, 4.398198344}
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