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Simplifying (5x2 + -2x + -29) + (3x2 + 9x) = 0 Reorder the terms: (-29 + -2x + 5x2) + (3x2 + 9x) = 0 Remove parenthesis around (-29 + -2x + 5x2) -29 + -2x + 5x2 + (3x2 + 9x) = 0 Reorder the terms: -29 + -2x + 5x2 + (9x + 3x2) = 0 Remove parenthesis around (9x + 3x2) -29 + -2x + 5x2 + 9x + 3x2 = 0 Reorder the terms: -29 + -2x + 9x + 5x2 + 3x2 = 0 Combine like terms: -2x + 9x = 7x -29 + 7x + 5x2 + 3x2 = 0 Combine like terms: 5x2 + 3x2 = 8x2 -29 + 7x + 8x2 = 0 Solving -29 + 7x + 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'. -3.625 + 0.875x + x2 = 0 Move the constant term to the right: Add '3.625' to each side of the equation. -3.625 + 0.875x + 3.625 + x2 = 0 + 3.625 Reorder the terms: -3.625 + 3.625 + 0.875x + x2 = 0 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + 0.875x + x2 = 0 + 3.625 0.875x + x2 = 0 + 3.625 Combine like terms: 0 + 3.625 = 3.625 0.875x + x2 = 3.625 The x term is 0.875x. Take half its coefficient (0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. 0.875x + 0.19140625 + x2 = 3.625 + 0.19140625 Reorder the terms: 0.19140625 + 0.875x + x2 = 3.625 + 0.19140625 Combine like terms: 3.625 + 0.19140625 = 3.81640625 0.19140625 + 0.875x + x2 = 3.81640625 Factor a perfect square on the left side: (x + 0.4375)(x + 0.4375) = 3.81640625 Calculate the square root of the right side: 1.953562451 Break this problem into two subproblems by setting (x + 0.4375) equal to 1.953562451 and -1.953562451.Subproblem 1
x + 0.4375 = 1.953562451 Simplifying x + 0.4375 = 1.953562451 Reorder the terms: 0.4375 + x = 1.953562451 Solving 0.4375 + x = 1.953562451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + x = 1.953562451 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + x = 1.953562451 + -0.4375 x = 1.953562451 + -0.4375 Combine like terms: 1.953562451 + -0.4375 = 1.516062451 x = 1.516062451 Simplifying x = 1.516062451Subproblem 2
x + 0.4375 = -1.953562451 Simplifying x + 0.4375 = -1.953562451 Reorder the terms: 0.4375 + x = -1.953562451 Solving 0.4375 + x = -1.953562451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + x = -1.953562451 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + x = -1.953562451 + -0.4375 x = -1.953562451 + -0.4375 Combine like terms: -1.953562451 + -0.4375 = -2.391062451 x = -2.391062451 Simplifying x = -2.391062451Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.516062451, -2.391062451}
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