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Simplifying -5x2 + 120x + 1000 = 0 Reorder the terms: 1000 + 120x + -5x2 = 0 Solving 1000 + 120x + -5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(200 + 24x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(200 + 24x + -1x2)' equal to zero and attempt to solve: Simplifying 200 + 24x + -1x2 = 0 Solving 200 + 24x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -200 + -24x + x2 = 0 Move the constant term to the right: Add '200' to each side of the equation. -200 + -24x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + -24x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + -24x + x2 = 0 + 200 -24x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 -24x + x2 = 200 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = 200 + 144 Reorder the terms: 144 + -24x + x2 = 200 + 144 Combine like terms: 200 + 144 = 344 144 + -24x + x2 = 344 Factor a perfect square on the left side: (x + -12)(x + -12) = 344 Calculate the square root of the right side: 18.547236991 Break this problem into two subproblems by setting (x + -12) equal to 18.547236991 and -18.547236991.Subproblem 1
x + -12 = 18.547236991 Simplifying x + -12 = 18.547236991 Reorder the terms: -12 + x = 18.547236991 Solving -12 + x = 18.547236991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 18.547236991 + 12 Combine like terms: -12 + 12 = 0 0 + x = 18.547236991 + 12 x = 18.547236991 + 12 Combine like terms: 18.547236991 + 12 = 30.547236991 x = 30.547236991 Simplifying x = 30.547236991Subproblem 2
x + -12 = -18.547236991 Simplifying x + -12 = -18.547236991 Reorder the terms: -12 + x = -18.547236991 Solving -12 + x = -18.547236991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -18.547236991 + 12 Combine like terms: -12 + 12 = 0 0 + x = -18.547236991 + 12 x = -18.547236991 + 12 Combine like terms: -18.547236991 + 12 = -6.547236991 x = -6.547236991 Simplifying x = -6.547236991Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.547236991, -6.547236991}Solution
x = {30.547236991, -6.547236991}
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