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Simplifying 5x + 5 = 4x2 + -100 Reorder the terms: 5 + 5x = 4x2 + -100 Reorder the terms: 5 + 5x = -100 + 4x2 Solving 5 + 5x = -100 + 4x2 Solving for variable 'x'. Reorder the terms: 5 + 100 + 5x + -4x2 = -100 + 4x2 + 100 + -4x2 Combine like terms: 5 + 100 = 105 105 + 5x + -4x2 = -100 + 4x2 + 100 + -4x2 Reorder the terms: 105 + 5x + -4x2 = -100 + 100 + 4x2 + -4x2 Combine like terms: -100 + 100 = 0 105 + 5x + -4x2 = 0 + 4x2 + -4x2 105 + 5x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 105 + 5x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -26.25 + -1.25x + x2 = 0 Move the constant term to the right: Add '26.25' to each side of the equation. -26.25 + -1.25x + 26.25 + x2 = 0 + 26.25 Reorder the terms: -26.25 + 26.25 + -1.25x + x2 = 0 + 26.25 Combine like terms: -26.25 + 26.25 = 0.00 0.00 + -1.25x + x2 = 0 + 26.25 -1.25x + x2 = 0 + 26.25 Combine like terms: 0 + 26.25 = 26.25 -1.25x + x2 = 26.25 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = 26.25 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 26.25 + 0.390625 Combine like terms: 26.25 + 0.390625 = 26.640625 0.390625 + -1.25x + x2 = 26.640625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 26.640625 Calculate the square root of the right side: 5.161455706 Break this problem into two subproblems by setting (x + -0.625) equal to 5.161455706 and -5.161455706.Subproblem 1
x + -0.625 = 5.161455706 Simplifying x + -0.625 = 5.161455706 Reorder the terms: -0.625 + x = 5.161455706 Solving -0.625 + x = 5.161455706 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 5.161455706 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 5.161455706 + 0.625 x = 5.161455706 + 0.625 Combine like terms: 5.161455706 + 0.625 = 5.786455706 x = 5.786455706 Simplifying x = 5.786455706Subproblem 2
x + -0.625 = -5.161455706 Simplifying x + -0.625 = -5.161455706 Reorder the terms: -0.625 + x = -5.161455706 Solving -0.625 + x = -5.161455706 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -5.161455706 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -5.161455706 + 0.625 x = -5.161455706 + 0.625 Combine like terms: -5.161455706 + 0.625 = -4.536455706 x = -4.536455706 Simplifying x = -4.536455706Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.786455706, -4.536455706}
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