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Simplifying 0 = 2x2 + -1x + -64 Reorder the terms: 0 = -64 + -1x + 2x2 Solving 0 = -64 + -1x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 64 = 64 64 + x + -2x2 = -64 + -1x + 2x2 + 64 + x + -2x2 Reorder the terms: 64 + x + -2x2 = -64 + 64 + -1x + x + 2x2 + -2x2 Combine like terms: -64 + 64 = 0 64 + x + -2x2 = 0 + -1x + x + 2x2 + -2x2 64 + x + -2x2 = -1x + x + 2x2 + -2x2 Combine like terms: -1x + x = 0 64 + x + -2x2 = 0 + 2x2 + -2x2 64 + x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 64 + x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -32 + -0.5x + x2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + -0.5x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + -0.5x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -0.5x + x2 = 0 + 32 -0.5x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 -0.5x + x2 = 32 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.5x + 0.25 + x2 = 32 + 0.25 Reorder the terms: 0.25 + -0.5x + x2 = 32 + 0.25 Combine like terms: 32 + 0.25 = 32.25 0.25 + -0.5x + x2 = 32.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (x + 0.5) equal to 5.678908346 and -5.678908346.Subproblem 1
x + 0.5 = 5.678908346 Simplifying x + 0.5 = 5.678908346 Reorder the terms: 0.5 + x = 5.678908346 Solving 0.5 + x = 5.678908346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 5.678908346 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.678908346 + -0.5 x = 5.678908346 + -0.5 Combine like terms: 5.678908346 + -0.5 = 5.178908346 x = 5.178908346 Simplifying x = 5.178908346Subproblem 2
x + 0.5 = -5.678908346 Simplifying x + 0.5 = -5.678908346 Reorder the terms: 0.5 + x = -5.678908346 Solving 0.5 + x = -5.678908346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -5.678908346 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.678908346 + -0.5 x = -5.678908346 + -0.5 Combine like terms: -5.678908346 + -0.5 = -6.178908346 x = -6.178908346 Simplifying x = -6.178908346Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.178908346, -6.178908346}
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