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Simplifying 32x2 + 16x + -51 = 0 Reorder the terms: -51 + 16x + 32x2 = 0 Solving -51 + 16x + 32x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -1.59375 + 0.5x + x2 = 0 Move the constant term to the right: Add '1.59375' to each side of the equation. -1.59375 + 0.5x + 1.59375 + x2 = 0 + 1.59375 Reorder the terms: -1.59375 + 1.59375 + 0.5x + x2 = 0 + 1.59375 Combine like terms: -1.59375 + 1.59375 = 0.00000 0.00000 + 0.5x + x2 = 0 + 1.59375 0.5x + x2 = 0 + 1.59375 Combine like terms: 0 + 1.59375 = 1.59375 0.5x + x2 = 1.59375 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 1.59375 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 1.59375 + 0.0625 Combine like terms: 1.59375 + 0.0625 = 1.65625 0.0625 + 0.5x + x2 = 1.65625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 1.65625 Calculate the square root of the right side: 1.286953768 Break this problem into two subproblems by setting (x + 0.25) equal to 1.286953768 and -1.286953768.Subproblem 1
x + 0.25 = 1.286953768 Simplifying x + 0.25 = 1.286953768 Reorder the terms: 0.25 + x = 1.286953768 Solving 0.25 + x = 1.286953768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.286953768 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.286953768 + -0.25 x = 1.286953768 + -0.25 Combine like terms: 1.286953768 + -0.25 = 1.036953768 x = 1.036953768 Simplifying x = 1.036953768Subproblem 2
x + 0.25 = -1.286953768 Simplifying x + 0.25 = -1.286953768 Reorder the terms: 0.25 + x = -1.286953768 Solving 0.25 + x = -1.286953768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.286953768 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.286953768 + -0.25 x = -1.286953768 + -0.25 Combine like terms: -1.286953768 + -0.25 = -1.536953768 x = -1.536953768 Simplifying x = -1.536953768Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.036953768, -1.536953768}
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