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Simplifying x2 + -425x + 7500 = 0 Reorder the terms: 7500 + -425x + x2 = 0 Solving 7500 + -425x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-7500' to each side of the equation. 7500 + -425x + -7500 + x2 = 0 + -7500 Reorder the terms: 7500 + -7500 + -425x + x2 = 0 + -7500 Combine like terms: 7500 + -7500 = 0 0 + -425x + x2 = 0 + -7500 -425x + x2 = 0 + -7500 Combine like terms: 0 + -7500 = -7500 -425x + x2 = -7500 The x term is -425x. Take half its coefficient (-212.5). Square it (45156.25) and add it to both sides. Add '45156.25' to each side of the equation. -425x + 45156.25 + x2 = -7500 + 45156.25 Reorder the terms: 45156.25 + -425x + x2 = -7500 + 45156.25 Combine like terms: -7500 + 45156.25 = 37656.25 45156.25 + -425x + x2 = 37656.25 Factor a perfect square on the left side: (x + -212.5)(x + -212.5) = 37656.25 Calculate the square root of the right side: 194.052183703 Break this problem into two subproblems by setting (x + -212.5) equal to 194.052183703 and -194.052183703.Subproblem 1
x + -212.5 = 194.052183703 Simplifying x + -212.5 = 194.052183703 Reorder the terms: -212.5 + x = 194.052183703 Solving -212.5 + x = 194.052183703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '212.5' to each side of the equation. -212.5 + 212.5 + x = 194.052183703 + 212.5 Combine like terms: -212.5 + 212.5 = 0.0 0.0 + x = 194.052183703 + 212.5 x = 194.052183703 + 212.5 Combine like terms: 194.052183703 + 212.5 = 406.552183703 x = 406.552183703 Simplifying x = 406.552183703Subproblem 2
x + -212.5 = -194.052183703 Simplifying x + -212.5 = -194.052183703 Reorder the terms: -212.5 + x = -194.052183703 Solving -212.5 + x = -194.052183703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '212.5' to each side of the equation. -212.5 + 212.5 + x = -194.052183703 + 212.5 Combine like terms: -212.5 + 212.5 = 0.0 0.0 + x = -194.052183703 + 212.5 x = -194.052183703 + 212.5 Combine like terms: -194.052183703 + 212.5 = 18.447816297 x = 18.447816297 Simplifying x = 18.447816297Solution
The solution to the problem is based on the solutions from the subproblems. x = {406.552183703, 18.447816297}
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