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Simplifying 16x2 + x = 1132 Reorder the terms: x + 16x2 = 1132 Solving x + 16x2 = 1132 Solving for variable 'x'. Reorder the terms: -1132 + x + 16x2 = 1132 + -1132 Combine like terms: 1132 + -1132 = 0 -1132 + x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -70.75 + 0.0625x + x2 = 0 Move the constant term to the right: Add '70.75' to each side of the equation. -70.75 + 0.0625x + 70.75 + x2 = 0 + 70.75 Reorder the terms: -70.75 + 70.75 + 0.0625x + x2 = 0 + 70.75 Combine like terms: -70.75 + 70.75 = 0.00 0.00 + 0.0625x + x2 = 0 + 70.75 0.0625x + x2 = 0 + 70.75 Combine like terms: 0 + 70.75 = 70.75 0.0625x + x2 = 70.75 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. 0.0625x + 0.25 + x2 = 70.75 + 0.25 Reorder the terms: 0.25 + 0.0625x + x2 = 70.75 + 0.25 Combine like terms: 70.75 + 0.25 = 71 0.25 + 0.0625x + x2 = 71 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 71 Calculate the square root of the right side: 8.426149773 Break this problem into two subproblems by setting (x + 0.5) equal to 8.426149773 and -8.426149773.Subproblem 1
x + 0.5 = 8.426149773 Simplifying x + 0.5 = 8.426149773 Reorder the terms: 0.5 + x = 8.426149773 Solving 0.5 + x = 8.426149773 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 = 8.426149773 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 8.426149773 + -0.5 x = 8.426149773 + -0.5 Combine like terms: 8.426149773 + -0.5 = 7.926149773 x = 7.926149773 Simplifying x = 7.926149773Subproblem 2
x + 0.5 = -8.426149773 Simplifying x + 0.5 = -8.426149773 Reorder the terms: 0.5 + x = -8.426149773 Solving 0.5 + x = -8.426149773 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 = -8.426149773 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -8.426149773 + -0.5 x = -8.426149773 + -0.5 Combine like terms: -8.426149773 + -0.5 = -8.926149773 x = -8.926149773 Simplifying x = -8.926149773Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.926149773, -8.926149773}
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