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Simplifying 220 = 16x2 + 10x Reorder the terms: 220 = 10x + 16x2 Solving 220 = 10x + 16x2 Solving for variable 'x'. Reorder the terms: 220 + -10x + -16x2 = 10x + -10x + 16x2 + -16x2 Combine like terms: 10x + -10x = 0 220 + -10x + -16x2 = 0 + 16x2 + -16x2 220 + -10x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 220 + -10x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(110 + -5x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(110 + -5x + -8x2)' equal to zero and attempt to solve: Simplifying 110 + -5x + -8x2 = 0 Solving 110 + -5x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -13.75 + 0.625x + x2 = 0 Move the constant term to the right: Add '13.75' to each side of the equation. -13.75 + 0.625x + 13.75 + x2 = 0 + 13.75 Reorder the terms: -13.75 + 13.75 + 0.625x + x2 = 0 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + 0.625x + x2 = 0 + 13.75 0.625x + x2 = 0 + 13.75 Combine like terms: 0 + 13.75 = 13.75 0.625x + x2 = 13.75 The x term is 0.625x. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625x + 0.09765625 + x2 = 13.75 + 0.09765625 Reorder the terms: 0.09765625 + 0.625x + x2 = 13.75 + 0.09765625 Combine like terms: 13.75 + 0.09765625 = 13.84765625 0.09765625 + 0.625x + x2 = 13.84765625 Factor a perfect square on the left side: (x + 0.3125)(x + 0.3125) = 13.84765625 Calculate the square root of the right side: 3.721243912 Break this problem into two subproblems by setting (x + 0.3125) equal to 3.721243912 and -3.721243912.Subproblem 1
x + 0.3125 = 3.721243912 Simplifying x + 0.3125 = 3.721243912 Reorder the terms: 0.3125 + x = 3.721243912 Solving 0.3125 + x = 3.721243912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + x = 3.721243912 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x = 3.721243912 + -0.3125 x = 3.721243912 + -0.3125 Combine like terms: 3.721243912 + -0.3125 = 3.408743912 x = 3.408743912 Simplifying x = 3.408743912Subproblem 2
x + 0.3125 = -3.721243912 Simplifying x + 0.3125 = -3.721243912 Reorder the terms: 0.3125 + x = -3.721243912 Solving 0.3125 + x = -3.721243912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + x = -3.721243912 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x = -3.721243912 + -0.3125 x = -3.721243912 + -0.3125 Combine like terms: -3.721243912 + -0.3125 = -4.033743912 x = -4.033743912 Simplifying x = -4.033743912Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.408743912, -4.033743912}Solution
x = {3.408743912, -4.033743912}
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