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Simplifying 4x2 + -5x = 100x + -1x + 2 Reorder the terms: -5x + 4x2 = 100x + -1x + 2 Reorder the terms: -5x + 4x2 = 2 + 100x + -1x Combine like terms: 100x + -1x = 99x -5x + 4x2 = 2 + 99x Solving -5x + 4x2 = 2 + 99x Solving for variable 'x'. Reorder the terms: -2 + -5x + -99x + 4x2 = 2 + 99x + -2 + -99x Combine like terms: -5x + -99x = -104x -2 + -104x + 4x2 = 2 + 99x + -2 + -99x Reorder the terms: -2 + -104x + 4x2 = 2 + -2 + 99x + -99x Combine like terms: 2 + -2 = 0 -2 + -104x + 4x2 = 0 + 99x + -99x -2 + -104x + 4x2 = 99x + -99x Combine like terms: 99x + -99x = 0 -2 + -104x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -52x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -52x + 2x2)' equal to zero and attempt to solve: Simplifying -1 + -52x + 2x2 = 0 Solving -1 + -52x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -26x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -26x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -26x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -26x + x2 = 0 + 0.5 -26x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -26x + x2 = 0.5 The x term is -26x. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x + 169 + x2 = 0.5 + 169 Reorder the terms: 169 + -26x + x2 = 0.5 + 169 Combine like terms: 0.5 + 169 = 169.5 169 + -26x + x2 = 169.5 Factor a perfect square on the left side: (x + -13)(x + -13) = 169.5 Calculate the square root of the right side: 13.019216566 Break this problem into two subproblems by setting (x + -13) equal to 13.019216566 and -13.019216566.Subproblem 1
x + -13 = 13.019216566 Simplifying x + -13 = 13.019216566 Reorder the terms: -13 + x = 13.019216566 Solving -13 + x = 13.019216566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 13.019216566 + 13 Combine like terms: -13 + 13 = 0 0 + x = 13.019216566 + 13 x = 13.019216566 + 13 Combine like terms: 13.019216566 + 13 = 26.019216566 x = 26.019216566 Simplifying x = 26.019216566Subproblem 2
x + -13 = -13.019216566 Simplifying x + -13 = -13.019216566 Reorder the terms: -13 + x = -13.019216566 Solving -13 + x = -13.019216566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -13.019216566 + 13 Combine like terms: -13 + 13 = 0 0 + x = -13.019216566 + 13 x = -13.019216566 + 13 Combine like terms: -13.019216566 + 13 = -0.019216566 x = -0.019216566 Simplifying x = -0.019216566Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.019216566, -0.019216566}Solution
x = {26.019216566, -0.019216566}
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