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Simplifying 4x2 + -60x + -70 = 0 Reorder the terms: -70 + -60x + 4x2 = 0 Solving -70 + -60x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-35 + -30x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-35 + -30x + 2x2)' equal to zero and attempt to solve: Simplifying -35 + -30x + 2x2 = 0 Solving -35 + -30x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -17.5 + -15x + x2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + -15x + 17.5 + x2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + -15x + x2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + -15x + x2 = 0 + 17.5 -15x + x2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 -15x + x2 = 17.5 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 = 17.5 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 17.5 + 56.25 Combine like terms: 17.5 + 56.25 = 73.75 56.25 + -15x + x2 = 73.75 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 73.75 Calculate the square root of the right side: 8.587782019 Break this problem into two subproblems by setting (x + -7.5) equal to 8.587782019 and -8.587782019.Subproblem 1
x + -7.5 = 8.587782019 Simplifying x + -7.5 = 8.587782019 Reorder the terms: -7.5 + x = 8.587782019 Solving -7.5 + x = 8.587782019 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 = 8.587782019 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 8.587782019 + 7.5 x = 8.587782019 + 7.5 Combine like terms: 8.587782019 + 7.5 = 16.087782019 x = 16.087782019 Simplifying x = 16.087782019Subproblem 2
x + -7.5 = -8.587782019 Simplifying x + -7.5 = -8.587782019 Reorder the terms: -7.5 + x = -8.587782019 Solving -7.5 + x = -8.587782019 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 = -8.587782019 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -8.587782019 + 7.5 x = -8.587782019 + 7.5 Combine like terms: -8.587782019 + 7.5 = -1.087782019 x = -1.087782019 Simplifying x = -1.087782019Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.087782019, -1.087782019}Solution
x = {16.087782019, -1.087782019}
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