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Simplifying 0 = 10x2 + -275x + -2200 Reorder the terms: 0 = -2200 + -275x + 10x2 Solving 0 = -2200 + -275x + 10x2 Solving for variable 'x'. Combine like terms: 0 + 2200 = 2200 2200 + 275x + -10x2 = -2200 + -275x + 10x2 + 2200 + 275x + -10x2 Reorder the terms: 2200 + 275x + -10x2 = -2200 + 2200 + -275x + 275x + 10x2 + -10x2 Combine like terms: -2200 + 2200 = 0 2200 + 275x + -10x2 = 0 + -275x + 275x + 10x2 + -10x2 2200 + 275x + -10x2 = -275x + 275x + 10x2 + -10x2 Combine like terms: -275x + 275x = 0 2200 + 275x + -10x2 = 0 + 10x2 + -10x2 2200 + 275x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 2200 + 275x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(440 + 55x + -2x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(440 + 55x + -2x2)' equal to zero and attempt to solve: Simplifying 440 + 55x + -2x2 = 0 Solving 440 + 55x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -220 + -27.5x + x2 = 0 Move the constant term to the right: Add '220' to each side of the equation. -220 + -27.5x + 220 + x2 = 0 + 220 Reorder the terms: -220 + 220 + -27.5x + x2 = 0 + 220 Combine like terms: -220 + 220 = 0 0 + -27.5x + x2 = 0 + 220 -27.5x + x2 = 0 + 220 Combine like terms: 0 + 220 = 220 -27.5x + x2 = 220 The x term is -27.5x. Take half its coefficient (-13.75). Square it (189.0625) and add it to both sides. Add '189.0625' to each side of the equation. -27.5x + 189.0625 + x2 = 220 + 189.0625 Reorder the terms: 189.0625 + -27.5x + x2 = 220 + 189.0625 Combine like terms: 220 + 189.0625 = 409.0625 189.0625 + -27.5x + x2 = 409.0625 Factor a perfect square on the left side: (x + -13.75)(x + -13.75) = 409.0625 Calculate the square root of the right side: 20.22529357 Break this problem into two subproblems by setting (x + -13.75) equal to 20.22529357 and -20.22529357.Subproblem 1
x + -13.75 = 20.22529357 Simplifying x + -13.75 = 20.22529357 Reorder the terms: -13.75 + x = 20.22529357 Solving -13.75 + x = 20.22529357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.75' to each side of the equation. -13.75 + 13.75 + x = 20.22529357 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + x = 20.22529357 + 13.75 x = 20.22529357 + 13.75 Combine like terms: 20.22529357 + 13.75 = 33.97529357 x = 33.97529357 Simplifying x = 33.97529357Subproblem 2
x + -13.75 = -20.22529357 Simplifying x + -13.75 = -20.22529357 Reorder the terms: -13.75 + x = -20.22529357 Solving -13.75 + x = -20.22529357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.75' to each side of the equation. -13.75 + 13.75 + x = -20.22529357 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + x = -20.22529357 + 13.75 x = -20.22529357 + 13.75 Combine like terms: -20.22529357 + 13.75 = -6.47529357 x = -6.47529357 Simplifying x = -6.47529357Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.97529357, -6.47529357}Solution
x = {33.97529357, -6.47529357}
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