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Simplifying 4x2 + -60x + 100 = 0 Reorder the terms: 100 + -60x + 4x2 = 0 Solving 100 + -60x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(25 + -15x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(25 + -15x + x2)' equal to zero and attempt to solve: Simplifying 25 + -15x + x2 = 0 Solving 25 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -15x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -15x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -15x + x2 = 0 + -25 -15x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -15x + x2 = -25 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 = -25 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -25 + 56.25 Combine like terms: -25 + 56.25 = 31.25 56.25 + -15x + x2 = 31.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (x + -7.5) equal to 5.590169944 and -5.590169944.Subproblem 1
x + -7.5 = 5.590169944 Simplifying x + -7.5 = 5.590169944 Reorder the terms: -7.5 + x = 5.590169944 Solving -7.5 + x = 5.590169944 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 = 5.590169944 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 5.590169944 + 7.5 x = 5.590169944 + 7.5 Combine like terms: 5.590169944 + 7.5 = 13.090169944 x = 13.090169944 Simplifying x = 13.090169944Subproblem 2
x + -7.5 = -5.590169944 Simplifying x + -7.5 = -5.590169944 Reorder the terms: -7.5 + x = -5.590169944 Solving -7.5 + x = -5.590169944 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 = -5.590169944 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -5.590169944 + 7.5 x = -5.590169944 + 7.5 Combine like terms: -5.590169944 + 7.5 = 1.909830056 x = 1.909830056 Simplifying x = 1.909830056Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.090169944, 1.909830056}Solution
x = {13.090169944, 1.909830056}
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