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Simplifying 2x2 + -32x + -45 = 0 Reorder the terms: -45 + -32x + 2x2 = 0 Solving -45 + -32x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -22.5 + -16x + x2 = 0 Move the constant term to the right: Add '22.5' to each side of the equation. -22.5 + -16x + 22.5 + x2 = 0 + 22.5 Reorder the terms: -22.5 + 22.5 + -16x + x2 = 0 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + -16x + x2 = 0 + 22.5 -16x + x2 = 0 + 22.5 Combine like terms: 0 + 22.5 = 22.5 -16x + x2 = 22.5 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = 22.5 + 64 Reorder the terms: 64 + -16x + x2 = 22.5 + 64 Combine like terms: 22.5 + 64 = 86.5 64 + -16x + x2 = 86.5 Factor a perfect square on the left side: (x + -8)(x + -8) = 86.5 Calculate the square root of the right side: 9.300537619 Break this problem into two subproblems by setting (x + -8) equal to 9.300537619 and -9.300537619.Subproblem 1
x + -8 = 9.300537619 Simplifying x + -8 = 9.300537619 Reorder the terms: -8 + x = 9.300537619 Solving -8 + x = 9.300537619 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 9.300537619 + 8 Combine like terms: -8 + 8 = 0 0 + x = 9.300537619 + 8 x = 9.300537619 + 8 Combine like terms: 9.300537619 + 8 = 17.300537619 x = 17.300537619 Simplifying x = 17.300537619Subproblem 2
x + -8 = -9.300537619 Simplifying x + -8 = -9.300537619 Reorder the terms: -8 + x = -9.300537619 Solving -8 + x = -9.300537619 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -9.300537619 + 8 Combine like terms: -8 + 8 = 0 0 + x = -9.300537619 + 8 x = -9.300537619 + 8 Combine like terms: -9.300537619 + 8 = -1.300537619 x = -1.300537619 Simplifying x = -1.300537619Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.300537619, -1.300537619}
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