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Simplifying -1x = x(4x + -20) + -56 Reorder the terms: -1x = x(-20 + 4x) + -56 -1x = (-20 * x + 4x * x) + -56 -1x = (-20x + 4x2) + -56 Reorder the terms: -1x = -56 + -20x + 4x2 Solving -1x = -56 + -20x + 4x2 Solving for variable 'x'. Reorder the terms: 56 + -1x + 20x + -4x2 = -56 + -20x + 4x2 + 56 + 20x + -4x2 Combine like terms: -1x + 20x = 19x 56 + 19x + -4x2 = -56 + -20x + 4x2 + 56 + 20x + -4x2 Reorder the terms: 56 + 19x + -4x2 = -56 + 56 + -20x + 20x + 4x2 + -4x2 Combine like terms: -56 + 56 = 0 56 + 19x + -4x2 = 0 + -20x + 20x + 4x2 + -4x2 56 + 19x + -4x2 = -20x + 20x + 4x2 + -4x2 Combine like terms: -20x + 20x = 0 56 + 19x + -4x2 = 0 + 4x2 + -4x2 56 + 19x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 56 + 19x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -14 + -4.75x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + -4.75x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + -4.75x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -4.75x + x2 = 0 + 14 -4.75x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 -4.75x + x2 = 14 The x term is -4.75x. Take half its coefficient (-2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. -4.75x + 5.640625 + x2 = 14 + 5.640625 Reorder the terms: 5.640625 + -4.75x + x2 = 14 + 5.640625 Combine like terms: 14 + 5.640625 = 19.640625 5.640625 + -4.75x + x2 = 19.640625 Factor a perfect square on the left side: (x + -2.375)(x + -2.375) = 19.640625 Calculate the square root of the right side: 4.431774475 Break this problem into two subproblems by setting (x + -2.375) equal to 4.431774475 and -4.431774475.Subproblem 1
x + -2.375 = 4.431774475 Simplifying x + -2.375 = 4.431774475 Reorder the terms: -2.375 + x = 4.431774475 Solving -2.375 + x = 4.431774475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = 4.431774475 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = 4.431774475 + 2.375 x = 4.431774475 + 2.375 Combine like terms: 4.431774475 + 2.375 = 6.806774475 x = 6.806774475 Simplifying x = 6.806774475Subproblem 2
x + -2.375 = -4.431774475 Simplifying x + -2.375 = -4.431774475 Reorder the terms: -2.375 + x = -4.431774475 Solving -2.375 + x = -4.431774475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = -4.431774475 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = -4.431774475 + 2.375 x = -4.431774475 + 2.375 Combine like terms: -4.431774475 + 2.375 = -2.056774475 x = -2.056774475 Simplifying x = -2.056774475Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.806774475, -2.056774475}
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