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Simplifying (2x2 + 3x + -9) + -1(-4x + 7) = 0 Reorder the terms: (-9 + 3x + 2x2) + -1(-4x + 7) = 0 Remove parenthesis around (-9 + 3x + 2x2) -9 + 3x + 2x2 + -1(-4x + 7) = 0 Reorder the terms: -9 + 3x + 2x2 + -1(7 + -4x) = 0 -9 + 3x + 2x2 + (7 * -1 + -4x * -1) = 0 -9 + 3x + 2x2 + (-7 + 4x) = 0 Reorder the terms: -9 + -7 + 3x + 4x + 2x2 = 0 Combine like terms: -9 + -7 = -16 -16 + 3x + 4x + 2x2 = 0 Combine like terms: 3x + 4x = 7x -16 + 7x + 2x2 = 0 Solving -16 + 7x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -8 + 3.5x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 3.5x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 3.5x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 3.5x + x2 = 0 + 8 3.5x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 3.5x + x2 = 8 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 8 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 8 + 3.0625 Combine like terms: 8 + 3.0625 = 11.0625 3.0625 + 3.5x + x2 = 11.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 11.0625 Calculate the square root of the right side: 3.326033674 Break this problem into two subproblems by setting (x + 1.75) equal to 3.326033674 and -3.326033674.Subproblem 1
x + 1.75 = 3.326033674 Simplifying x + 1.75 = 3.326033674 Reorder the terms: 1.75 + x = 3.326033674 Solving 1.75 + x = 3.326033674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 3.326033674 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 3.326033674 + -1.75 x = 3.326033674 + -1.75 Combine like terms: 3.326033674 + -1.75 = 1.576033674 x = 1.576033674 Simplifying x = 1.576033674Subproblem 2
x + 1.75 = -3.326033674 Simplifying x + 1.75 = -3.326033674 Reorder the terms: 1.75 + x = -3.326033674 Solving 1.75 + x = -3.326033674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -3.326033674 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -3.326033674 + -1.75 x = -3.326033674 + -1.75 Combine like terms: -3.326033674 + -1.75 = -5.076033674 x = -5.076033674 Simplifying x = -5.076033674Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.576033674, -5.076033674}
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