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Simplifying 81 = 8x2 + -100x + 325 Reorder the terms: 81 = 325 + -100x + 8x2 Solving 81 = 325 + -100x + 8x2 Solving for variable 'x'. Combine like terms: 81 + -325 = -244 -244 + 100x + -8x2 = 325 + -100x + 8x2 + -325 + 100x + -8x2 Reorder the terms: -244 + 100x + -8x2 = 325 + -325 + -100x + 100x + 8x2 + -8x2 Combine like terms: 325 + -325 = 0 -244 + 100x + -8x2 = 0 + -100x + 100x + 8x2 + -8x2 -244 + 100x + -8x2 = -100x + 100x + 8x2 + -8x2 Combine like terms: -100x + 100x = 0 -244 + 100x + -8x2 = 0 + 8x2 + -8x2 -244 + 100x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -244 + 100x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-61 + 25x + -2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-61 + 25x + -2x2)' equal to zero and attempt to solve: Simplifying -61 + 25x + -2x2 = 0 Solving -61 + 25x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 30.5 + -12.5x + x2 = 0 Move the constant term to the right: Add '-30.5' to each side of the equation. 30.5 + -12.5x + -30.5 + x2 = 0 + -30.5 Reorder the terms: 30.5 + -30.5 + -12.5x + x2 = 0 + -30.5 Combine like terms: 30.5 + -30.5 = 0.0 0.0 + -12.5x + x2 = 0 + -30.5 -12.5x + x2 = 0 + -30.5 Combine like terms: 0 + -30.5 = -30.5 -12.5x + x2 = -30.5 The x term is -12.5x. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5x + 39.0625 + x2 = -30.5 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = -30.5 + 39.0625 Combine like terms: -30.5 + 39.0625 = 8.5625 39.0625 + -12.5x + x2 = 8.5625 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 8.5625 Calculate the square root of the right side: 2.926174978 Break this problem into two subproblems by setting (x + -6.25) equal to 2.926174978 and -2.926174978.Subproblem 1
x + -6.25 = 2.926174978 Simplifying x + -6.25 = 2.926174978 Reorder the terms: -6.25 + x = 2.926174978 Solving -6.25 + x = 2.926174978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 2.926174978 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 2.926174978 + 6.25 x = 2.926174978 + 6.25 Combine like terms: 2.926174978 + 6.25 = 9.176174978 x = 9.176174978 Simplifying x = 9.176174978Subproblem 2
x + -6.25 = -2.926174978 Simplifying x + -6.25 = -2.926174978 Reorder the terms: -6.25 + x = -2.926174978 Solving -6.25 + x = -2.926174978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -2.926174978 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -2.926174978 + 6.25 x = -2.926174978 + 6.25 Combine like terms: -2.926174978 + 6.25 = 3.323825022 x = 3.323825022 Simplifying x = 3.323825022Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.176174978, 3.323825022}Solution
x = {9.176174978, 3.323825022}
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