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Simplifying -16x2 + 10x + 725 = 0 Reorder the terms: 725 + 10x + -16x2 = 0 Solving 725 + 10x + -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'. -45.3125 + -0.625x + x2 = 0 Move the constant term to the right: Add '45.3125' to each side of the equation. -45.3125 + -0.625x + 45.3125 + x2 = 0 + 45.3125 Reorder the terms: -45.3125 + 45.3125 + -0.625x + x2 = 0 + 45.3125 Combine like terms: -45.3125 + 45.3125 = 0.0000 0.0000 + -0.625x + x2 = 0 + 45.3125 -0.625x + x2 = 0 + 45.3125 Combine like terms: 0 + 45.3125 = 45.3125 -0.625x + x2 = 45.3125 The x term is -0.625x. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625x + 0.09765625 + x2 = 45.3125 + 0.09765625 Reorder the terms: 0.09765625 + -0.625x + x2 = 45.3125 + 0.09765625 Combine like terms: 45.3125 + 0.09765625 = 45.41015625 0.09765625 + -0.625x + x2 = 45.41015625 Factor a perfect square on the left side: (x + -0.3125)(x + -0.3125) = 45.41015625 Calculate the square root of the right side: 6.738705829 Break this problem into two subproblems by setting (x + -0.3125) equal to 6.738705829 and -6.738705829.Subproblem 1
x + -0.3125 = 6.738705829 Simplifying x + -0.3125 = 6.738705829 Reorder the terms: -0.3125 + x = 6.738705829 Solving -0.3125 + x = 6.738705829 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = 6.738705829 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = 6.738705829 + 0.3125 x = 6.738705829 + 0.3125 Combine like terms: 6.738705829 + 0.3125 = 7.051205829 x = 7.051205829 Simplifying x = 7.051205829Subproblem 2
x + -0.3125 = -6.738705829 Simplifying x + -0.3125 = -6.738705829 Reorder the terms: -0.3125 + x = -6.738705829 Solving -0.3125 + x = -6.738705829 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = -6.738705829 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = -6.738705829 + 0.3125 x = -6.738705829 + 0.3125 Combine like terms: -6.738705829 + 0.3125 = -6.426205829 x = -6.426205829 Simplifying x = -6.426205829Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.051205829, -6.426205829}
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