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Simplifying (9x2 + -7x + -61) + (7x2 + 9x) = 0 Reorder the terms: (-61 + -7x + 9x2) + (7x2 + 9x) = 0 Remove parenthesis around (-61 + -7x + 9x2) -61 + -7x + 9x2 + (7x2 + 9x) = 0 Reorder the terms: -61 + -7x + 9x2 + (9x + 7x2) = 0 Remove parenthesis around (9x + 7x2) -61 + -7x + 9x2 + 9x + 7x2 = 0 Reorder the terms: -61 + -7x + 9x + 9x2 + 7x2 = 0 Combine like terms: -7x + 9x = 2x -61 + 2x + 9x2 + 7x2 = 0 Combine like terms: 9x2 + 7x2 = 16x2 -61 + 2x + 16x2 = 0 Solving -61 + 2x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -3.8125 + 0.125x + x2 = 0 Move the constant term to the right: Add '3.8125' to each side of the equation. -3.8125 + 0.125x + 3.8125 + x2 = 0 + 3.8125 Reorder the terms: -3.8125 + 3.8125 + 0.125x + x2 = 0 + 3.8125 Combine like terms: -3.8125 + 3.8125 = 0.0000 0.0000 + 0.125x + x2 = 0 + 3.8125 0.125x + x2 = 0 + 3.8125 Combine like terms: 0 + 3.8125 = 3.8125 0.125x + x2 = 3.8125 The x term is 0.125x. Take half its coefficient (0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. 0.125x + 0.00390625 + x2 = 3.8125 + 0.00390625 Reorder the terms: 0.00390625 + 0.125x + x2 = 3.8125 + 0.00390625 Combine like terms: 3.8125 + 0.00390625 = 3.81640625 0.00390625 + 0.125x + x2 = 3.81640625 Factor a perfect square on the left side: (x + 0.0625)(x + 0.0625) = 3.81640625 Calculate the square root of the right side: 1.953562451 Break this problem into two subproblems by setting (x + 0.0625) equal to 1.953562451 and -1.953562451.Subproblem 1
x + 0.0625 = 1.953562451 Simplifying x + 0.0625 = 1.953562451 Reorder the terms: 0.0625 + x = 1.953562451 Solving 0.0625 + x = 1.953562451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + x = 1.953562451 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = 1.953562451 + -0.0625 x = 1.953562451 + -0.0625 Combine like terms: 1.953562451 + -0.0625 = 1.891062451 x = 1.891062451 Simplifying x = 1.891062451Subproblem 2
x + 0.0625 = -1.953562451 Simplifying x + 0.0625 = -1.953562451 Reorder the terms: 0.0625 + x = -1.953562451 Solving 0.0625 + x = -1.953562451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + x = -1.953562451 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = -1.953562451 + -0.0625 x = -1.953562451 + -0.0625 Combine like terms: -1.953562451 + -0.0625 = -2.016062451 x = -2.016062451 Simplifying x = -2.016062451Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.891062451, -2.016062451}
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