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Simplifying 5x2 + 40x + -8 = 0 Reorder the terms: -8 + 40x + 5x2 = 0 Solving -8 + 40x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.6 + 8x + x2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + 8x + 1.6 + x2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + 8x + x2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + 8x + x2 = 0 + 1.6 8x + x2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 8x + x2 = 1.6 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 1.6 + 16 Reorder the terms: 16 + 8x + x2 = 1.6 + 16 Combine like terms: 1.6 + 16 = 17.6 16 + 8x + x2 = 17.6 Factor a perfect square on the left side: (x + 4)(x + 4) = 17.6 Calculate the square root of the right side: 4.195235393 Break this problem into two subproblems by setting (x + 4) equal to 4.195235393 and -4.195235393.Subproblem 1
x + 4 = 4.195235393 Simplifying x + 4 = 4.195235393 Reorder the terms: 4 + x = 4.195235393 Solving 4 + x = 4.195235393 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 4.195235393 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.195235393 + -4 x = 4.195235393 + -4 Combine like terms: 4.195235393 + -4 = 0.195235393 x = 0.195235393 Simplifying x = 0.195235393Subproblem 2
x + 4 = -4.195235393 Simplifying x + 4 = -4.195235393 Reorder the terms: 4 + x = -4.195235393 Solving 4 + x = -4.195235393 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -4.195235393 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.195235393 + -4 x = -4.195235393 + -4 Combine like terms: -4.195235393 + -4 = -8.195235393 x = -8.195235393 Simplifying x = -8.195235393Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.195235393, -8.195235393}
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