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Simplifying -16x2 + -1x + 1156 = 0 Reorder the terms: 1156 + -1x + -16x2 = 0 Solving 1156 + -1x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -72.25 + 0.0625x + x2 = 0 Move the constant term to the right: Add '72.25' to each side of the equation. -72.25 + 0.0625x + 72.25 + x2 = 0 + 72.25 Reorder the terms: -72.25 + 72.25 + 0.0625x + x2 = 0 + 72.25 Combine like terms: -72.25 + 72.25 = 0.00 0.00 + 0.0625x + x2 = 0 + 72.25 0.0625x + x2 = 0 + 72.25 Combine like terms: 0 + 72.25 = 72.25 0.0625x + x2 = 72.25 The x term is 0.0625x. Take half its coefficient (0.03125). Square it (0.0009765625) and add it to both sides. Add '0.0009765625' to each side of the equation. 0.0625x + 0.0009765625 + x2 = 72.25 + 0.0009765625 Reorder the terms: 0.0009765625 + 0.0625x + x2 = 72.25 + 0.0009765625 Combine like terms: 72.25 + 0.0009765625 = 72.2509765625 0.0009765625 + 0.0625x + x2 = 72.2509765625 Factor a perfect square on the left side: (x + 0.03125)(x + 0.03125) = 72.2509765625 Calculate the square root of the right side: 8.500057445 Break this problem into two subproblems by setting (x + 0.03125) equal to 8.500057445 and -8.500057445.Subproblem 1
x + 0.03125 = 8.500057445 Simplifying x + 0.03125 = 8.500057445 Reorder the terms: 0.03125 + x = 8.500057445 Solving 0.03125 + x = 8.500057445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03125' to each side of the equation. 0.03125 + -0.03125 + x = 8.500057445 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + x = 8.500057445 + -0.03125 x = 8.500057445 + -0.03125 Combine like terms: 8.500057445 + -0.03125 = 8.468807445 x = 8.468807445 Simplifying x = 8.468807445Subproblem 2
x + 0.03125 = -8.500057445 Simplifying x + 0.03125 = -8.500057445 Reorder the terms: 0.03125 + x = -8.500057445 Solving 0.03125 + x = -8.500057445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03125' to each side of the equation. 0.03125 + -0.03125 + x = -8.500057445 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + x = -8.500057445 + -0.03125 x = -8.500057445 + -0.03125 Combine like terms: -8.500057445 + -0.03125 = -8.531307445 x = -8.531307445 Simplifying x = -8.531307445Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.468807445, -8.531307445}
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