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Simplifying 5x2 + -90x + -520 = 0 Reorder the terms: -520 + -90x + 5x2 = 0 Solving -520 + -90x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-104 + -18x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-104 + -18x + x2)' equal to zero and attempt to solve: Simplifying -104 + -18x + x2 = 0 Solving -104 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '104' to each side of the equation. -104 + -18x + 104 + x2 = 0 + 104 Reorder the terms: -104 + 104 + -18x + x2 = 0 + 104 Combine like terms: -104 + 104 = 0 0 + -18x + x2 = 0 + 104 -18x + x2 = 0 + 104 Combine like terms: 0 + 104 = 104 -18x + x2 = 104 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = 104 + 81 Reorder the terms: 81 + -18x + x2 = 104 + 81 Combine like terms: 104 + 81 = 185 81 + -18x + x2 = 185 Factor a perfect square on the left side: (x + -9)(x + -9) = 185 Calculate the square root of the right side: 13.601470509 Break this problem into two subproblems by setting (x + -9) equal to 13.601470509 and -13.601470509.Subproblem 1
x + -9 = 13.601470509 Simplifying x + -9 = 13.601470509 Reorder the terms: -9 + x = 13.601470509 Solving -9 + x = 13.601470509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 13.601470509 + 9 Combine like terms: -9 + 9 = 0 0 + x = 13.601470509 + 9 x = 13.601470509 + 9 Combine like terms: 13.601470509 + 9 = 22.601470509 x = 22.601470509 Simplifying x = 22.601470509Subproblem 2
x + -9 = -13.601470509 Simplifying x + -9 = -13.601470509 Reorder the terms: -9 + x = -13.601470509 Solving -9 + x = -13.601470509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -13.601470509 + 9 Combine like terms: -9 + 9 = 0 0 + x = -13.601470509 + 9 x = -13.601470509 + 9 Combine like terms: -13.601470509 + 9 = -4.601470509 x = -4.601470509 Simplifying x = -4.601470509Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.601470509, -4.601470509}Solution
x = {22.601470509, -4.601470509}
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