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Simplifying -16x2 + -5x + 500 = 0 Reorder the terms: 500 + -5x + -16x2 = 0 Solving 500 + -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'. -31.25 + 0.3125x + x2 = 0 Move the constant term to the right: Add '31.25' to each side of the equation. -31.25 + 0.3125x + 31.25 + x2 = 0 + 31.25 Reorder the terms: -31.25 + 31.25 + 0.3125x + x2 = 0 + 31.25 Combine like terms: -31.25 + 31.25 = 0.00 0.00 + 0.3125x + x2 = 0 + 31.25 0.3125x + x2 = 0 + 31.25 Combine like terms: 0 + 31.25 = 31.25 0.3125x + x2 = 31.25 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 = 31.25 + 0.0244140625 Reorder the terms: 0.0244140625 + 0.3125x + x2 = 31.25 + 0.0244140625 Combine like terms: 31.25 + 0.0244140625 = 31.2744140625 0.0244140625 + 0.3125x + x2 = 31.2744140625 Factor a perfect square on the left side: (x + 0.15625)(x + 0.15625) = 31.2744140625 Calculate the square root of the right side: 5.592353178 Break this problem into two subproblems by setting (x + 0.15625) equal to 5.592353178 and -5.592353178.Subproblem 1
x + 0.15625 = 5.592353178 Simplifying x + 0.15625 = 5.592353178 Reorder the terms: 0.15625 + x = 5.592353178 Solving 0.15625 + x = 5.592353178 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 = 5.592353178 + -0.15625 Combine like terms: 0.15625 + -0.15625 = 0.00000 0.00000 + x = 5.592353178 + -0.15625 x = 5.592353178 + -0.15625 Combine like terms: 5.592353178 + -0.15625 = 5.436103178 x = 5.436103178 Simplifying x = 5.436103178Subproblem 2
x + 0.15625 = -5.592353178 Simplifying x + 0.15625 = -5.592353178 Reorder the terms: 0.15625 + x = -5.592353178 Solving 0.15625 + x = -5.592353178 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 = -5.592353178 + -0.15625 Combine like terms: 0.15625 + -0.15625 = 0.00000 0.00000 + x = -5.592353178 + -0.15625 x = -5.592353178 + -0.15625 Combine like terms: -5.592353178 + -0.15625 = -5.748603178 x = -5.748603178 Simplifying x = -5.748603178Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.436103178, -5.748603178}
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