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Simplifying 5x + 8x2 + -52 = 0 Reorder the terms: -52 + 5x + 8x2 = 0 Solving -52 + 5x + 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'. -6.5 + 0.625x + x2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + 0.625x + 6.5 + x2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + 0.625x + x2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + 0.625x + x2 = 0 + 6.5 0.625x + x2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 0.625x + x2 = 6.5 The x term is 0.625x. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625x + 0.09765625 + x2 = 6.5 + 0.09765625 Reorder the terms: 0.09765625 + 0.625x + x2 = 6.5 + 0.09765625 Combine like terms: 6.5 + 0.09765625 = 6.59765625 0.09765625 + 0.625x + x2 = 6.59765625 Factor a perfect square on the left side: (x + 0.3125)(x + 0.3125) = 6.59765625 Calculate the square root of the right side: 2.568590324 Break this problem into two subproblems by setting (x + 0.3125) equal to 2.568590324 and -2.568590324.Subproblem 1
x + 0.3125 = 2.568590324 Simplifying x + 0.3125 = 2.568590324 Reorder the terms: 0.3125 + x = 2.568590324 Solving 0.3125 + x = 2.568590324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + x = 2.568590324 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x = 2.568590324 + -0.3125 x = 2.568590324 + -0.3125 Combine like terms: 2.568590324 + -0.3125 = 2.256090324 x = 2.256090324 Simplifying x = 2.256090324Subproblem 2
x + 0.3125 = -2.568590324 Simplifying x + 0.3125 = -2.568590324 Reorder the terms: 0.3125 + x = -2.568590324 Solving 0.3125 + x = -2.568590324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + x = -2.568590324 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x = -2.568590324 + -0.3125 x = -2.568590324 + -0.3125 Combine like terms: -2.568590324 + -0.3125 = -2.881090324 x = -2.881090324 Simplifying x = -2.881090324Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.256090324, -2.881090324}
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