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Simplifying 2x2 + -32x + 111 = 0 Reorder the terms: 111 + -32x + 2x2 = 0 Solving 111 + -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'. 55.5 + -16x + x2 = 0 Move the constant term to the right: Add '-55.5' to each side of the equation. 55.5 + -16x + -55.5 + x2 = 0 + -55.5 Reorder the terms: 55.5 + -55.5 + -16x + x2 = 0 + -55.5 Combine like terms: 55.5 + -55.5 = 0.0 0.0 + -16x + x2 = 0 + -55.5 -16x + x2 = 0 + -55.5 Combine like terms: 0 + -55.5 = -55.5 -16x + x2 = -55.5 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 = -55.5 + 64 Reorder the terms: 64 + -16x + x2 = -55.5 + 64 Combine like terms: -55.5 + 64 = 8.5 64 + -16x + x2 = 8.5 Factor a perfect square on the left side: (x + -8)(x + -8) = 8.5 Calculate the square root of the right side: 2.915475947 Break this problem into two subproblems by setting (x + -8) equal to 2.915475947 and -2.915475947.Subproblem 1
x + -8 = 2.915475947 Simplifying x + -8 = 2.915475947 Reorder the terms: -8 + x = 2.915475947 Solving -8 + x = 2.915475947 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 = 2.915475947 + 8 Combine like terms: -8 + 8 = 0 0 + x = 2.915475947 + 8 x = 2.915475947 + 8 Combine like terms: 2.915475947 + 8 = 10.915475947 x = 10.915475947 Simplifying x = 10.915475947Subproblem 2
x + -8 = -2.915475947 Simplifying x + -8 = -2.915475947 Reorder the terms: -8 + x = -2.915475947 Solving -8 + x = -2.915475947 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 = -2.915475947 + 8 Combine like terms: -8 + 8 = 0 0 + x = -2.915475947 + 8 x = -2.915475947 + 8 Combine like terms: -2.915475947 + 8 = 5.084524053 x = 5.084524053 Simplifying x = 5.084524053Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.915475947, 5.084524053}
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