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Simplifying 8x2 + 40x + 29 = 0 Reorder the terms: 29 + 40x + 8x2 = 0 Solving 29 + 40x + 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 + 5x + x2 = 0 Move the constant term to the right: Add '-3.625' to each side of the equation. 3.625 + 5x + -3.625 + x2 = 0 + -3.625 Reorder the terms: 3.625 + -3.625 + 5x + x2 = 0 + -3.625 Combine like terms: 3.625 + -3.625 = 0.000 0.000 + 5x + x2 = 0 + -3.625 5x + x2 = 0 + -3.625 Combine like terms: 0 + -3.625 = -3.625 5x + x2 = -3.625 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -3.625 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -3.625 + 6.25 Combine like terms: -3.625 + 6.25 = 2.625 6.25 + 5x + x2 = 2.625 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 2.625 Calculate the square root of the right side: 1.620185175 Break this problem into two subproblems by setting (x + 2.5) equal to 1.620185175 and -1.620185175.Subproblem 1
x + 2.5 = 1.620185175 Simplifying x + 2.5 = 1.620185175 Reorder the terms: 2.5 + x = 1.620185175 Solving 2.5 + x = 1.620185175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 1.620185175 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 1.620185175 + -2.5 x = 1.620185175 + -2.5 Combine like terms: 1.620185175 + -2.5 = -0.879814825 x = -0.879814825 Simplifying x = -0.879814825Subproblem 2
x + 2.5 = -1.620185175 Simplifying x + 2.5 = -1.620185175 Reorder the terms: 2.5 + x = -1.620185175 Solving 2.5 + x = -1.620185175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -1.620185175 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -1.620185175 + -2.5 x = -1.620185175 + -2.5 Combine like terms: -1.620185175 + -2.5 = -4.120185175 x = -4.120185175 Simplifying x = -4.120185175Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.879814825, -4.120185175}
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