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Simplifying 10x2 + 225x + -1400 = 0 Reorder the terms: -1400 + 225x + 10x2 = 0 Solving -1400 + 225x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-280 + 45x + 2x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-280 + 45x + 2x2)' equal to zero and attempt to solve: Simplifying -280 + 45x + 2x2 = 0 Solving -280 + 45x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -140 + 22.5x + x2 = 0 Move the constant term to the right: Add '140' to each side of the equation. -140 + 22.5x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + 22.5x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + 22.5x + x2 = 0 + 140 22.5x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 22.5x + x2 = 140 The x term is 22.5x. Take half its coefficient (11.25). Square it (126.5625) and add it to both sides. Add '126.5625' to each side of the equation. 22.5x + 126.5625 + x2 = 140 + 126.5625 Reorder the terms: 126.5625 + 22.5x + x2 = 140 + 126.5625 Combine like terms: 140 + 126.5625 = 266.5625 126.5625 + 22.5x + x2 = 266.5625 Factor a perfect square on the left side: (x + 11.25)(x + 11.25) = 266.5625 Calculate the square root of the right side: 16.326741867 Break this problem into two subproblems by setting (x + 11.25) equal to 16.326741867 and -16.326741867.Subproblem 1
x + 11.25 = 16.326741867 Simplifying x + 11.25 = 16.326741867 Reorder the terms: 11.25 + x = 16.326741867 Solving 11.25 + x = 16.326741867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.25' to each side of the equation. 11.25 + -11.25 + x = 16.326741867 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = 16.326741867 + -11.25 x = 16.326741867 + -11.25 Combine like terms: 16.326741867 + -11.25 = 5.076741867 x = 5.076741867 Simplifying x = 5.076741867Subproblem 2
x + 11.25 = -16.326741867 Simplifying x + 11.25 = -16.326741867 Reorder the terms: 11.25 + x = -16.326741867 Solving 11.25 + x = -16.326741867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.25' to each side of the equation. 11.25 + -11.25 + x = -16.326741867 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = -16.326741867 + -11.25 x = -16.326741867 + -11.25 Combine like terms: -16.326741867 + -11.25 = -27.576741867 x = -27.576741867 Simplifying x = -27.576741867Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.076741867, -27.576741867}Solution
x = {5.076741867, -27.576741867}
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