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Simplifying -2x2 + 400x + -110 = 0 Reorder the terms: -110 + 400x + -2x2 = 0 Solving -110 + 400x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-55 + 200x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-55 + 200x + -1x2)' equal to zero and attempt to solve: Simplifying -55 + 200x + -1x2 = 0 Solving -55 + 200x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 55 + -200x + x2 = 0 Move the constant term to the right: Add '-55' to each side of the equation. 55 + -200x + -55 + x2 = 0 + -55 Reorder the terms: 55 + -55 + -200x + x2 = 0 + -55 Combine like terms: 55 + -55 = 0 0 + -200x + x2 = 0 + -55 -200x + x2 = 0 + -55 Combine like terms: 0 + -55 = -55 -200x + x2 = -55 The x term is -200x. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200x + 10000 + x2 = -55 + 10000 Reorder the terms: 10000 + -200x + x2 = -55 + 10000 Combine like terms: -55 + 10000 = 9945 10000 + -200x + x2 = 9945 Factor a perfect square on the left side: (x + -100)(x + -100) = 9945 Calculate the square root of the right side: 99.724620832 Break this problem into two subproblems by setting (x + -100) equal to 99.724620832 and -99.724620832.Subproblem 1
x + -100 = 99.724620832 Simplifying x + -100 = 99.724620832 Reorder the terms: -100 + x = 99.724620832 Solving -100 + x = 99.724620832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = 99.724620832 + 100 Combine like terms: -100 + 100 = 0 0 + x = 99.724620832 + 100 x = 99.724620832 + 100 Combine like terms: 99.724620832 + 100 = 199.724620832 x = 199.724620832 Simplifying x = 199.724620832Subproblem 2
x + -100 = -99.724620832 Simplifying x + -100 = -99.724620832 Reorder the terms: -100 + x = -99.724620832 Solving -100 + x = -99.724620832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = -99.724620832 + 100 Combine like terms: -100 + 100 = 0 0 + x = -99.724620832 + 100 x = -99.724620832 + 100 Combine like terms: -99.724620832 + 100 = 0.275379168 x = 0.275379168 Simplifying x = 0.275379168Solution
The solution to the problem is based on the solutions from the subproblems. x = {199.724620832, 0.275379168}Solution
x = {199.724620832, 0.275379168}
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