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Simplifying 72x2 + -8x + -90 = 0 Reorder the terms: -90 + -8x + 72x2 = 0 Solving -90 + -8x + 72x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-45 + -4x + 36x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-45 + -4x + 36x2)' equal to zero and attempt to solve: Simplifying -45 + -4x + 36x2 = 0 Solving -45 + -4x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -1.25 + -0.1111111111x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -0.1111111111x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -0.1111111111x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -0.1111111111x + x2 = 0 + 1.25 -0.1111111111x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -0.1111111111x + x2 = 1.25 The x term is -0.1111111111x. Take half its coefficient (-0.05555555555). Square it (0.003086419752) and add it to both sides. Add '0.003086419752' to each side of the equation. -0.1111111111x + 0.003086419752 + x2 = 1.25 + 0.003086419752 Reorder the terms: 0.003086419752 + -0.1111111111x + x2 = 1.25 + 0.003086419752 Combine like terms: 1.25 + 0.003086419752 = 1.253086419752 0.003086419752 + -0.1111111111x + x2 = 1.253086419752 Factor a perfect square on the left side: (x + -0.05555555555)(x + -0.05555555555) = 1.253086419752 Calculate the square root of the right side: 1.119413427 Break this problem into two subproblems by setting (x + -0.05555555555) equal to 1.119413427 and -1.119413427.Subproblem 1
x + -0.05555555555 = 1.119413427 Simplifying x + -0.05555555555 = 1.119413427 Reorder the terms: -0.05555555555 + x = 1.119413427 Solving -0.05555555555 + x = 1.119413427 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + x = 1.119413427 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = 1.119413427 + 0.05555555555 x = 1.119413427 + 0.05555555555 Combine like terms: 1.119413427 + 0.05555555555 = 1.17496898255 x = 1.17496898255 Simplifying x = 1.17496898255Subproblem 2
x + -0.05555555555 = -1.119413427 Simplifying x + -0.05555555555 = -1.119413427 Reorder the terms: -0.05555555555 + x = -1.119413427 Solving -0.05555555555 + x = -1.119413427 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + x = -1.119413427 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = -1.119413427 + 0.05555555555 x = -1.119413427 + 0.05555555555 Combine like terms: -1.119413427 + 0.05555555555 = -1.06385787145 x = -1.06385787145 Simplifying x = -1.06385787145Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.17496898255, -1.06385787145}Solution
x = {1.17496898255, -1.06385787145}
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