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Simplifying 5x2 + -5x + -500 = 0 Reorder the terms: -500 + -5x + 5x2 = 0 Solving -500 + -5x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-100 + -1x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-100 + -1x + x2)' equal to zero and attempt to solve: Simplifying -100 + -1x + x2 = 0 Solving -100 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + -1x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + -1x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -1x + x2 = 0 + 100 -1x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 -1x + x2 = 100 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 100 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 100 + 0.25 Combine like terms: 100 + 0.25 = 100.25 0.25 + -1x + x2 = 100.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 100.25 Calculate the square root of the right side: 10.012492197 Break this problem into two subproblems by setting (x + -0.5) equal to 10.012492197 and -10.012492197.Subproblem 1
x + -0.5 = 10.012492197 Simplifying x + -0.5 = 10.012492197 Reorder the terms: -0.5 + x = 10.012492197 Solving -0.5 + x = 10.012492197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 10.012492197 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 10.012492197 + 0.5 x = 10.012492197 + 0.5 Combine like terms: 10.012492197 + 0.5 = 10.512492197 x = 10.512492197 Simplifying x = 10.512492197Subproblem 2
x + -0.5 = -10.012492197 Simplifying x + -0.5 = -10.012492197 Reorder the terms: -0.5 + x = -10.012492197 Solving -0.5 + x = -10.012492197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -10.012492197 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -10.012492197 + 0.5 x = -10.012492197 + 0.5 Combine like terms: -10.012492197 + 0.5 = -9.512492197 x = -9.512492197 Simplifying x = -9.512492197Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.512492197, -9.512492197}Solution
x = {10.512492197, -9.512492197}
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