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Simplifying (6x2 + 9x + -1) + -1(-2x2 + 6) = 0 Reorder the terms: (-1 + 9x + 6x2) + -1(-2x2 + 6) = 0 Remove parenthesis around (-1 + 9x + 6x2) -1 + 9x + 6x2 + -1(-2x2 + 6) = 0 Reorder the terms: -1 + 9x + 6x2 + -1(6 + -2x2) = 0 -1 + 9x + 6x2 + (6 * -1 + -2x2 * -1) = 0 -1 + 9x + 6x2 + (-6 + 2x2) = 0 Reorder the terms: -1 + -6 + 9x + 6x2 + 2x2 = 0 Combine like terms: -1 + -6 = -7 -7 + 9x + 6x2 + 2x2 = 0 Combine like terms: 6x2 + 2x2 = 8x2 -7 + 9x + 8x2 = 0 Solving -7 + 9x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.875 + 1.125x + x2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + 1.125x + 0.875 + x2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + 1.125x + x2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + 1.125x + x2 = 0 + 0.875 1.125x + x2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 1.125x + x2 = 0.875 The x term is 1.125x. Take half its coefficient (0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. 1.125x + 0.31640625 + x2 = 0.875 + 0.31640625 Reorder the terms: 0.31640625 + 1.125x + x2 = 0.875 + 0.31640625 Combine like terms: 0.875 + 0.31640625 = 1.19140625 0.31640625 + 1.125x + x2 = 1.19140625 Factor a perfect square on the left side: (x + 0.5625)(x + 0.5625) = 1.19140625 Calculate the square root of the right side: 1.091515575 Break this problem into two subproblems by setting (x + 0.5625) equal to 1.091515575 and -1.091515575.Subproblem 1
x + 0.5625 = 1.091515575 Simplifying x + 0.5625 = 1.091515575 Reorder the terms: 0.5625 + x = 1.091515575 Solving 0.5625 + x = 1.091515575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = 1.091515575 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = 1.091515575 + -0.5625 x = 1.091515575 + -0.5625 Combine like terms: 1.091515575 + -0.5625 = 0.529015575 x = 0.529015575 Simplifying x = 0.529015575Subproblem 2
x + 0.5625 = -1.091515575 Simplifying x + 0.5625 = -1.091515575 Reorder the terms: 0.5625 + x = -1.091515575 Solving 0.5625 + x = -1.091515575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = -1.091515575 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = -1.091515575 + -0.5625 x = -1.091515575 + -0.5625 Combine like terms: -1.091515575 + -0.5625 = -1.654015575 x = -1.654015575 Simplifying x = -1.654015575Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.529015575, -1.654015575}
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