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Simplifying (4x2 + 7x + -9) + -1(-2x2 + -4x + 6) = 0 Reorder the terms: (-9 + 7x + 4x2) + -1(-2x2 + -4x + 6) = 0 Remove parenthesis around (-9 + 7x + 4x2) -9 + 7x + 4x2 + -1(-2x2 + -4x + 6) = 0 Reorder the terms: -9 + 7x + 4x2 + -1(6 + -4x + -2x2) = 0 -9 + 7x + 4x2 + (6 * -1 + -4x * -1 + -2x2 * -1) = 0 -9 + 7x + 4x2 + (-6 + 4x + 2x2) = 0 Reorder the terms: -9 + -6 + 7x + 4x + 4x2 + 2x2 = 0 Combine like terms: -9 + -6 = -15 -15 + 7x + 4x + 4x2 + 2x2 = 0 Combine like terms: 7x + 4x = 11x -15 + 11x + 4x2 + 2x2 = 0 Combine like terms: 4x2 + 2x2 = 6x2 -15 + 11x + 6x2 = 0 Solving -15 + 11x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.5 + 1.833333333x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 1.833333333x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 1.833333333x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 1.833333333x + x2 = 0 + 2.5 1.833333333x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 1.833333333x + x2 = 2.5 The x term is 1.833333333x. Take half its coefficient (0.9166666665). Square it (0.8402777775) and add it to both sides. Add '0.8402777775' to each side of the equation. 1.833333333x + 0.8402777775 + x2 = 2.5 + 0.8402777775 Reorder the terms: 0.8402777775 + 1.833333333x + x2 = 2.5 + 0.8402777775 Combine like terms: 2.5 + 0.8402777775 = 3.3402777775 0.8402777775 + 1.833333333x + x2 = 3.3402777775 Factor a perfect square on the left side: (x + 0.9166666665)(x + 0.9166666665) = 3.3402777775 Calculate the square root of the right side: 1.827642683 Break this problem into two subproblems by setting (x + 0.9166666665) equal to 1.827642683 and -1.827642683.Subproblem 1
x + 0.9166666665 = 1.827642683 Simplifying x + 0.9166666665 = 1.827642683 Reorder the terms: 0.9166666665 + x = 1.827642683 Solving 0.9166666665 + x = 1.827642683 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9166666665' to each side of the equation. 0.9166666665 + -0.9166666665 + x = 1.827642683 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + x = 1.827642683 + -0.9166666665 x = 1.827642683 + -0.9166666665 Combine like terms: 1.827642683 + -0.9166666665 = 0.9109760165 x = 0.9109760165 Simplifying x = 0.9109760165Subproblem 2
x + 0.9166666665 = -1.827642683 Simplifying x + 0.9166666665 = -1.827642683 Reorder the terms: 0.9166666665 + x = -1.827642683 Solving 0.9166666665 + x = -1.827642683 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9166666665' to each side of the equation. 0.9166666665 + -0.9166666665 + x = -1.827642683 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + x = -1.827642683 + -0.9166666665 x = -1.827642683 + -0.9166666665 Combine like terms: -1.827642683 + -0.9166666665 = -2.7443093495 x = -2.7443093495 Simplifying x = -2.7443093495Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9109760165, -2.7443093495}
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