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Simplifying 5x2 + -60x + -90 = 0 Reorder the terms: -90 + -60x + 5x2 = 0 Solving -90 + -60x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-18 + -12x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-18 + -12x + x2)' equal to zero and attempt to solve: Simplifying -18 + -12x + x2 = 0 Solving -18 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -12x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -12x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -12x + x2 = 0 + 18 -12x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -12x + x2 = 18 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 18 + 36 Reorder the terms: 36 + -12x + x2 = 18 + 36 Combine like terms: 18 + 36 = 54 36 + -12x + x2 = 54 Factor a perfect square on the left side: (x + -6)(x + -6) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (x + -6) equal to 7.348469228 and -7.348469228.Subproblem 1
x + -6 = 7.348469228 Simplifying x + -6 = 7.348469228 Reorder the terms: -6 + x = 7.348469228 Solving -6 + x = 7.348469228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 7.348469228 + 6 Combine like terms: -6 + 6 = 0 0 + x = 7.348469228 + 6 x = 7.348469228 + 6 Combine like terms: 7.348469228 + 6 = 13.348469228 x = 13.348469228 Simplifying x = 13.348469228Subproblem 2
x + -6 = -7.348469228 Simplifying x + -6 = -7.348469228 Reorder the terms: -6 + x = -7.348469228 Solving -6 + x = -7.348469228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -7.348469228 + 6 Combine like terms: -6 + 6 = 0 0 + x = -7.348469228 + 6 x = -7.348469228 + 6 Combine like terms: -7.348469228 + 6 = -1.348469228 x = -1.348469228 Simplifying x = -1.348469228Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.348469228, -1.348469228}Solution
x = {13.348469228, -1.348469228}
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