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Simplifying 4x2 + -60x + 180 = 0 Reorder the terms: 180 + -60x + 4x2 = 0 Solving 180 + -60x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(45 + -15x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(45 + -15x + x2)' equal to zero and attempt to solve: Simplifying 45 + -15x + x2 = 0 Solving 45 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-45' to each side of the equation. 45 + -15x + -45 + x2 = 0 + -45 Reorder the terms: 45 + -45 + -15x + x2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -15x + x2 = 0 + -45 -15x + x2 = 0 + -45 Combine like terms: 0 + -45 = -45 -15x + x2 = -45 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -45 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -45 + 56.25 Combine like terms: -45 + 56.25 = 11.25 56.25 + -15x + x2 = 11.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (x + -7.5) equal to 3.354101966 and -3.354101966.Subproblem 1
x + -7.5 = 3.354101966 Simplifying x + -7.5 = 3.354101966 Reorder the terms: -7.5 + x = 3.354101966 Solving -7.5 + x = 3.354101966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 3.354101966 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 3.354101966 + 7.5 x = 3.354101966 + 7.5 Combine like terms: 3.354101966 + 7.5 = 10.854101966 x = 10.854101966 Simplifying x = 10.854101966Subproblem 2
x + -7.5 = -3.354101966 Simplifying x + -7.5 = -3.354101966 Reorder the terms: -7.5 + x = -3.354101966 Solving -7.5 + x = -3.354101966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -3.354101966 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -3.354101966 + 7.5 x = -3.354101966 + 7.5 Combine like terms: -3.354101966 + 7.5 = 4.145898034 x = 4.145898034 Simplifying x = 4.145898034Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.854101966, 4.145898034}Solution
x = {10.854101966, 4.145898034}
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