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Simplifying -32x2 + 19600x + -1764000 = 0 Reorder the terms: -1764000 + 19600x + -32x2 = 0 Solving -1764000 + 19600x + -32x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(-110250 + 1225x + -2x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-110250 + 1225x + -2x2)' equal to zero and attempt to solve: Simplifying -110250 + 1225x + -2x2 = 0 Solving -110250 + 1225x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 55125 + -612.5x + x2 = 0 Move the constant term to the right: Add '-55125' to each side of the equation. 55125 + -612.5x + -55125 + x2 = 0 + -55125 Reorder the terms: 55125 + -55125 + -612.5x + x2 = 0 + -55125 Combine like terms: 55125 + -55125 = 0 0 + -612.5x + x2 = 0 + -55125 -612.5x + x2 = 0 + -55125 Combine like terms: 0 + -55125 = -55125 -612.5x + x2 = -55125 The x term is -612.5x. Take half its coefficient (-306.25). Square it (93789.0625) and add it to both sides. Add '93789.0625' to each side of the equation. -612.5x + 93789.0625 + x2 = -55125 + 93789.0625 Reorder the terms: 93789.0625 + -612.5x + x2 = -55125 + 93789.0625 Combine like terms: -55125 + 93789.0625 = 38664.0625 93789.0625 + -612.5x + x2 = 38664.0625 Factor a perfect square on the left side: (x + -306.25)(x + -306.25) = 38664.0625 Calculate the square root of the right side: 196.631794225 Break this problem into two subproblems by setting (x + -306.25) equal to 196.631794225 and -196.631794225.Subproblem 1
x + -306.25 = 196.631794225 Simplifying x + -306.25 = 196.631794225 Reorder the terms: -306.25 + x = 196.631794225 Solving -306.25 + x = 196.631794225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '306.25' to each side of the equation. -306.25 + 306.25 + x = 196.631794225 + 306.25 Combine like terms: -306.25 + 306.25 = 0.00 0.00 + x = 196.631794225 + 306.25 x = 196.631794225 + 306.25 Combine like terms: 196.631794225 + 306.25 = 502.881794225 x = 502.881794225 Simplifying x = 502.881794225Subproblem 2
x + -306.25 = -196.631794225 Simplifying x + -306.25 = -196.631794225 Reorder the terms: -306.25 + x = -196.631794225 Solving -306.25 + x = -196.631794225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '306.25' to each side of the equation. -306.25 + 306.25 + x = -196.631794225 + 306.25 Combine like terms: -306.25 + 306.25 = 0.00 0.00 + x = -196.631794225 + 306.25 x = -196.631794225 + 306.25 Combine like terms: -196.631794225 + 306.25 = 109.618205775 x = 109.618205775 Simplifying x = 109.618205775Solution
The solution to the problem is based on the solutions from the subproblems. x = {502.881794225, 109.618205775}Solution
x = {502.881794225, 109.618205775}
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