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Simplifying 2x2 + -64x + 180 = 0 Reorder the terms: 180 + -64x + 2x2 = 0 Solving 180 + -64x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(90 + -32x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(90 + -32x + x2)' equal to zero and attempt to solve: Simplifying 90 + -32x + x2 = 0 Solving 90 + -32x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-90' to each side of the equation. 90 + -32x + -90 + x2 = 0 + -90 Reorder the terms: 90 + -90 + -32x + x2 = 0 + -90 Combine like terms: 90 + -90 = 0 0 + -32x + x2 = 0 + -90 -32x + x2 = 0 + -90 Combine like terms: 0 + -90 = -90 -32x + x2 = -90 The x term is -32x. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32x + 256 + x2 = -90 + 256 Reorder the terms: 256 + -32x + x2 = -90 + 256 Combine like terms: -90 + 256 = 166 256 + -32x + x2 = 166 Factor a perfect square on the left side: (x + -16)(x + -16) = 166 Calculate the square root of the right side: 12.884098727 Break this problem into two subproblems by setting (x + -16) equal to 12.884098727 and -12.884098727.Subproblem 1
x + -16 = 12.884098727 Simplifying x + -16 = 12.884098727 Reorder the terms: -16 + x = 12.884098727 Solving -16 + x = 12.884098727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 12.884098727 + 16 Combine like terms: -16 + 16 = 0 0 + x = 12.884098727 + 16 x = 12.884098727 + 16 Combine like terms: 12.884098727 + 16 = 28.884098727 x = 28.884098727 Simplifying x = 28.884098727Subproblem 2
x + -16 = -12.884098727 Simplifying x + -16 = -12.884098727 Reorder the terms: -16 + x = -12.884098727 Solving -16 + x = -12.884098727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = -12.884098727 + 16 Combine like terms: -16 + 16 = 0 0 + x = -12.884098727 + 16 x = -12.884098727 + 16 Combine like terms: -12.884098727 + 16 = 3.115901273 x = 3.115901273 Simplifying x = 3.115901273Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.884098727, 3.115901273}Solution
x = {28.884098727, 3.115901273}
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