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Simplifying 1125 + -5x + -16x2 = 0 Solving 1125 + -5x + -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'. -70.3125 + 0.3125x + x2 = 0 Move the constant term to the right: Add '70.3125' to each side of the equation. -70.3125 + 0.3125x + 70.3125 + x2 = 0 + 70.3125 Reorder the terms: -70.3125 + 70.3125 + 0.3125x + x2 = 0 + 70.3125 Combine like terms: -70.3125 + 70.3125 = 0.0000 0.0000 + 0.3125x + x2 = 0 + 70.3125 0.3125x + x2 = 0 + 70.3125 Combine like terms: 0 + 70.3125 = 70.3125 0.3125x + x2 = 70.3125 The x term is 0.3125x. Take half its coefficient (0.15625). Square it (0.0244140625) and add it to both sides. Add '0.0244140625' to each side of the equation. 0.3125x + 0.0244140625 + x2 = 70.3125 + 0.0244140625 Reorder the terms: 0.0244140625 + 0.3125x + x2 = 70.3125 + 0.0244140625 Combine like terms: 70.3125 + 0.0244140625 = 70.3369140625 0.0244140625 + 0.3125x + x2 = 70.3369140625 Factor a perfect square on the left side: (x + 0.15625)(x + 0.15625) = 70.3369140625 Calculate the square root of the right side: 8.386710563 Break this problem into two subproblems by setting (x + 0.15625) equal to 8.386710563 and -8.386710563.Subproblem 1
x + 0.15625 = 8.386710563 Simplifying x + 0.15625 = 8.386710563 Reorder the terms: 0.15625 + x = 8.386710563 Solving 0.15625 + x = 8.386710563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15625' to each side of the equation. 0.15625 + -0.15625 + x = 8.386710563 + -0.15625 Combine like terms: 0.15625 + -0.15625 = 0.00000 0.00000 + x = 8.386710563 + -0.15625 x = 8.386710563 + -0.15625 Combine like terms: 8.386710563 + -0.15625 = 8.230460563 x = 8.230460563 Simplifying x = 8.230460563Subproblem 2
x + 0.15625 = -8.386710563 Simplifying x + 0.15625 = -8.386710563 Reorder the terms: 0.15625 + x = -8.386710563 Solving 0.15625 + x = -8.386710563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15625' to each side of the equation. 0.15625 + -0.15625 + x = -8.386710563 + -0.15625 Combine like terms: 0.15625 + -0.15625 = 0.00000 0.00000 + x = -8.386710563 + -0.15625 x = -8.386710563 + -0.15625 Combine like terms: -8.386710563 + -0.15625 = -8.542960563 x = -8.542960563 Simplifying x = -8.542960563Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.230460563, -8.542960563}
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