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Simplifying 250x + -4x2 = 150 Solving 250x + -4x2 = 150 Solving for variable 'x'. Reorder the terms: -150 + 250x + -4x2 = 150 + -150 Combine like terms: 150 + -150 = 0 -150 + 250x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-75 + 125x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-75 + 125x + -2x2)' equal to zero and attempt to solve: Simplifying -75 + 125x + -2x2 = 0 Solving -75 + 125x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 37.5 + -62.5x + x2 = 0 Move the constant term to the right: Add '-37.5' to each side of the equation. 37.5 + -62.5x + -37.5 + x2 = 0 + -37.5 Reorder the terms: 37.5 + -37.5 + -62.5x + x2 = 0 + -37.5 Combine like terms: 37.5 + -37.5 = 0.0 0.0 + -62.5x + x2 = 0 + -37.5 -62.5x + x2 = 0 + -37.5 Combine like terms: 0 + -37.5 = -37.5 -62.5x + x2 = -37.5 The x term is -62.5x. Take half its coefficient (-31.25). Square it (976.5625) and add it to both sides. Add '976.5625' to each side of the equation. -62.5x + 976.5625 + x2 = -37.5 + 976.5625 Reorder the terms: 976.5625 + -62.5x + x2 = -37.5 + 976.5625 Combine like terms: -37.5 + 976.5625 = 939.0625 976.5625 + -62.5x + x2 = 939.0625 Factor a perfect square on the left side: (x + -31.25)(x + -31.25) = 939.0625 Calculate the square root of the right side: 30.64412668 Break this problem into two subproblems by setting (x + -31.25) equal to 30.64412668 and -30.64412668.Subproblem 1
x + -31.25 = 30.64412668 Simplifying x + -31.25 = 30.64412668 Reorder the terms: -31.25 + x = 30.64412668 Solving -31.25 + x = 30.64412668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31.25' to each side of the equation. -31.25 + 31.25 + x = 30.64412668 + 31.25 Combine like terms: -31.25 + 31.25 = 0.00 0.00 + x = 30.64412668 + 31.25 x = 30.64412668 + 31.25 Combine like terms: 30.64412668 + 31.25 = 61.89412668 x = 61.89412668 Simplifying x = 61.89412668Subproblem 2
x + -31.25 = -30.64412668 Simplifying x + -31.25 = -30.64412668 Reorder the terms: -31.25 + x = -30.64412668 Solving -31.25 + x = -30.64412668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31.25' to each side of the equation. -31.25 + 31.25 + x = -30.64412668 + 31.25 Combine like terms: -31.25 + 31.25 = 0.00 0.00 + x = -30.64412668 + 31.25 x = -30.64412668 + 31.25 Combine like terms: -30.64412668 + 31.25 = 0.60587332 x = 0.60587332 Simplifying x = 0.60587332Solution
The solution to the problem is based on the solutions from the subproblems. x = {61.89412668, 0.60587332}Solution
x = {61.89412668, 0.60587332}
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