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Simplifying 56x + -0.05x2 = 4x + 931.5 Reorder the terms: 56x + -0.05x2 = 931.5 + 4x Solving 56x + -0.05x2 = 931.5 + 4x Solving for variable 'x'. Reorder the terms: -931.5 + 56x + -4x + -0.05x2 = 931.5 + 4x + -931.5 + -4x Combine like terms: 56x + -4x = 52x -931.5 + 52x + -0.05x2 = 931.5 + 4x + -931.5 + -4x Reorder the terms: -931.5 + 52x + -0.05x2 = 931.5 + -931.5 + 4x + -4x Combine like terms: 931.5 + -931.5 = 0.0 -931.5 + 52x + -0.05x2 = 0.0 + 4x + -4x -931.5 + 52x + -0.05x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -931.5 + 52x + -0.05x2 = 0 Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. 18630 + -1040x + x2 = 0 Move the constant term to the right: Add '-18630' to each side of the equation. 18630 + -1040x + -18630 + x2 = 0 + -18630 Reorder the terms: 18630 + -18630 + -1040x + x2 = 0 + -18630 Combine like terms: 18630 + -18630 = 0 0 + -1040x + x2 = 0 + -18630 -1040x + x2 = 0 + -18630 Combine like terms: 0 + -18630 = -18630 -1040x + x2 = -18630 The x term is -1040x. Take half its coefficient (-520). Square it (270400) and add it to both sides. Add '270400' to each side of the equation. -1040x + 270400 + x2 = -18630 + 270400 Reorder the terms: 270400 + -1040x + x2 = -18630 + 270400 Combine like terms: -18630 + 270400 = 251770 270400 + -1040x + x2 = 251770 Factor a perfect square on the left side: (x + -520)(x + -520) = 251770 Calculate the square root of the right side: 501.766878142 Break this problem into two subproblems by setting (x + -520) equal to 501.766878142 and -501.766878142.Subproblem 1
x + -520 = 501.766878142 Simplifying x + -520 = 501.766878142 Reorder the terms: -520 + x = 501.766878142 Solving -520 + x = 501.766878142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '520' to each side of the equation. -520 + 520 + x = 501.766878142 + 520 Combine like terms: -520 + 520 = 0 0 + x = 501.766878142 + 520 x = 501.766878142 + 520 Combine like terms: 501.766878142 + 520 = 1021.766878142 x = 1021.766878142 Simplifying x = 1021.766878142Subproblem 2
x + -520 = -501.766878142 Simplifying x + -520 = -501.766878142 Reorder the terms: -520 + x = -501.766878142 Solving -520 + x = -501.766878142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '520' to each side of the equation. -520 + 520 + x = -501.766878142 + 520 Combine like terms: -520 + 520 = 0 0 + x = -501.766878142 + 520 x = -501.766878142 + 520 Combine like terms: -501.766878142 + 520 = 18.233121858 x = 18.233121858 Simplifying x = 18.233121858Solution
The solution to the problem is based on the solutions from the subproblems. x = {1021.766878142, 18.233121858}
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