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Simplifying -16x2 + 2x + 125 = 0 Reorder the terms: 125 + 2x + -16x2 = 0 Solving 125 + 2x + -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'. -7.8125 + -0.125x + x2 = 0 Move the constant term to the right: Add '7.8125' to each side of the equation. -7.8125 + -0.125x + 7.8125 + x2 = 0 + 7.8125 Reorder the terms: -7.8125 + 7.8125 + -0.125x + x2 = 0 + 7.8125 Combine like terms: -7.8125 + 7.8125 = 0.0000 0.0000 + -0.125x + x2 = 0 + 7.8125 -0.125x + x2 = 0 + 7.8125 Combine like terms: 0 + 7.8125 = 7.8125 -0.125x + x2 = 7.8125 The x term is -0.125x. Take half its coefficient (-0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. -0.125x + 0.00390625 + x2 = 7.8125 + 0.00390625 Reorder the terms: 0.00390625 + -0.125x + x2 = 7.8125 + 0.00390625 Combine like terms: 7.8125 + 0.00390625 = 7.81640625 0.00390625 + -0.125x + x2 = 7.81640625 Factor a perfect square on the left side: (x + -0.0625)(x + -0.0625) = 7.81640625 Calculate the square root of the right side: 2.795783656 Break this problem into two subproblems by setting (x + -0.0625) equal to 2.795783656 and -2.795783656.Subproblem 1
x + -0.0625 = 2.795783656 Simplifying x + -0.0625 = 2.795783656 Reorder the terms: -0.0625 + x = 2.795783656 Solving -0.0625 + x = 2.795783656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = 2.795783656 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = 2.795783656 + 0.0625 x = 2.795783656 + 0.0625 Combine like terms: 2.795783656 + 0.0625 = 2.858283656 x = 2.858283656 Simplifying x = 2.858283656Subproblem 2
x + -0.0625 = -2.795783656 Simplifying x + -0.0625 = -2.795783656 Reorder the terms: -0.0625 + x = -2.795783656 Solving -0.0625 + x = -2.795783656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = -2.795783656 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = -2.795783656 + 0.0625 x = -2.795783656 + 0.0625 Combine like terms: -2.795783656 + 0.0625 = -2.733283656 x = -2.733283656 Simplifying x = -2.733283656Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.858283656, -2.733283656}
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