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Simplifying 2x2 + 32x + -585 = 0 Reorder the terms: -585 + 32x + 2x2 = 0 Solving -585 + 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'. -292.5 + 16x + x2 = 0 Move the constant term to the right: Add '292.5' to each side of the equation. -292.5 + 16x + 292.5 + x2 = 0 + 292.5 Reorder the terms: -292.5 + 292.5 + 16x + x2 = 0 + 292.5 Combine like terms: -292.5 + 292.5 = 0.0 0.0 + 16x + x2 = 0 + 292.5 16x + x2 = 0 + 292.5 Combine like terms: 0 + 292.5 = 292.5 16x + x2 = 292.5 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 = 292.5 + 64 Reorder the terms: 64 + 16x + x2 = 292.5 + 64 Combine like terms: 292.5 + 64 = 356.5 64 + 16x + x2 = 356.5 Factor a perfect square on the left side: (x + 8)(x + 8) = 356.5 Calculate the square root of the right side: 18.881207588 Break this problem into two subproblems by setting (x + 8) equal to 18.881207588 and -18.881207588.Subproblem 1
x + 8 = 18.881207588 Simplifying x + 8 = 18.881207588 Reorder the terms: 8 + x = 18.881207588 Solving 8 + x = 18.881207588 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 = 18.881207588 + -8 Combine like terms: 8 + -8 = 0 0 + x = 18.881207588 + -8 x = 18.881207588 + -8 Combine like terms: 18.881207588 + -8 = 10.881207588 x = 10.881207588 Simplifying x = 10.881207588Subproblem 2
x + 8 = -18.881207588 Simplifying x + 8 = -18.881207588 Reorder the terms: 8 + x = -18.881207588 Solving 8 + x = -18.881207588 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 = -18.881207588 + -8 Combine like terms: 8 + -8 = 0 0 + x = -18.881207588 + -8 x = -18.881207588 + -8 Combine like terms: -18.881207588 + -8 = -26.881207588 x = -26.881207588 Simplifying x = -26.881207588Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.881207588, -26.881207588}
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