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Simplifying 4x2 + -250x + -450 = 0 Reorder the terms: -450 + -250x + 4x2 = 0 Solving -450 + -250x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-225 + -125x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-225 + -125x + 2x2)' equal to zero and attempt to solve: Simplifying -225 + -125x + 2x2 = 0 Solving -225 + -125x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -112.5 + -62.5x + x2 = 0 Move the constant term to the right: Add '112.5' to each side of the equation. -112.5 + -62.5x + 112.5 + x2 = 0 + 112.5 Reorder the terms: -112.5 + 112.5 + -62.5x + x2 = 0 + 112.5 Combine like terms: -112.5 + 112.5 = 0.0 0.0 + -62.5x + x2 = 0 + 112.5 -62.5x + x2 = 0 + 112.5 Combine like terms: 0 + 112.5 = 112.5 -62.5x + x2 = 112.5 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 = 112.5 + 976.5625 Reorder the terms: 976.5625 + -62.5x + x2 = 112.5 + 976.5625 Combine like terms: 112.5 + 976.5625 = 1089.0625 976.5625 + -62.5x + x2 = 1089.0625 Factor a perfect square on the left side: (x + -31.25)(x + -31.25) = 1089.0625 Calculate the square root of the right side: 33.000946956 Break this problem into two subproblems by setting (x + -31.25) equal to 33.000946956 and -33.000946956.Subproblem 1
x + -31.25 = 33.000946956 Simplifying x + -31.25 = 33.000946956 Reorder the terms: -31.25 + x = 33.000946956 Solving -31.25 + x = 33.000946956 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 = 33.000946956 + 31.25 Combine like terms: -31.25 + 31.25 = 0.00 0.00 + x = 33.000946956 + 31.25 x = 33.000946956 + 31.25 Combine like terms: 33.000946956 + 31.25 = 64.250946956 x = 64.250946956 Simplifying x = 64.250946956Subproblem 2
x + -31.25 = -33.000946956 Simplifying x + -31.25 = -33.000946956 Reorder the terms: -31.25 + x = -33.000946956 Solving -31.25 + x = -33.000946956 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 = -33.000946956 + 31.25 Combine like terms: -31.25 + 31.25 = 0.00 0.00 + x = -33.000946956 + 31.25 x = -33.000946956 + 31.25 Combine like terms: -33.000946956 + 31.25 = -1.750946956 x = -1.750946956 Simplifying x = -1.750946956Solution
The solution to the problem is based on the solutions from the subproblems. x = {64.250946956, -1.750946956}Solution
x = {64.250946956, -1.750946956}
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