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Simplifying 4x2 + -76x + -180 = 0 Reorder the terms: -180 + -76x + 4x2 = 0 Solving -180 + -76x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-45 + -19x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-45 + -19x + x2)' equal to zero and attempt to solve: Simplifying -45 + -19x + x2 = 0 Solving -45 + -19x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + -19x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + -19x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -19x + x2 = 0 + 45 -19x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 -19x + x2 = 45 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = 45 + 90.25 Reorder the terms: 90.25 + -19x + x2 = 45 + 90.25 Combine like terms: 45 + 90.25 = 135.25 90.25 + -19x + x2 = 135.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 135.25 Calculate the square root of the right side: 11.62970335 Break this problem into two subproblems by setting (x + -9.5) equal to 11.62970335 and -11.62970335.Subproblem 1
x + -9.5 = 11.62970335 Simplifying x + -9.5 = 11.62970335 Reorder the terms: -9.5 + x = 11.62970335 Solving -9.5 + x = 11.62970335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 11.62970335 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 11.62970335 + 9.5 x = 11.62970335 + 9.5 Combine like terms: 11.62970335 + 9.5 = 21.12970335 x = 21.12970335 Simplifying x = 21.12970335Subproblem 2
x + -9.5 = -11.62970335 Simplifying x + -9.5 = -11.62970335 Reorder the terms: -9.5 + x = -11.62970335 Solving -9.5 + x = -11.62970335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -11.62970335 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -11.62970335 + 9.5 x = -11.62970335 + 9.5 Combine like terms: -11.62970335 + 9.5 = -2.12970335 x = -2.12970335 Simplifying x = -2.12970335Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.12970335, -2.12970335}Solution
x = {21.12970335, -2.12970335}
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