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Simplifying 32x2 + -20x + 17 = 225 Reorder the terms: 17 + -20x + 32x2 = 225 Solving 17 + -20x + 32x2 = 225 Solving for variable 'x'. Reorder the terms: 17 + -225 + -20x + 32x2 = 225 + -225 Combine like terms: 17 + -225 = -208 -208 + -20x + 32x2 = 225 + -225 Combine like terms: 225 + -225 = 0 -208 + -20x + 32x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-52 + -5x + 8x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-52 + -5x + 8x2)' equal to zero and attempt to solve: Simplifying -52 + -5x + 8x2 = 0 Solving -52 + -5x + 8x2 = 0 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 = 2.881090324 x = 2.881090324 Simplifying x = 2.881090324Subproblem 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 = -2.256090324 x = -2.256090324 Simplifying x = -2.256090324Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.881090324, -2.256090324}Solution
x = {2.881090324, -2.256090324}
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