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Simplifying 0 = -16x2 + 5x + 40 Reorder the terms: 0 = 40 + 5x + -16x2 Solving 0 = 40 + 5x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -40 = -40 -40 + -5x + 16x2 = 40 + 5x + -16x2 + -40 + -5x + 16x2 Reorder the terms: -40 + -5x + 16x2 = 40 + -40 + 5x + -5x + -16x2 + 16x2 Combine like terms: 40 + -40 = 0 -40 + -5x + 16x2 = 0 + 5x + -5x + -16x2 + 16x2 -40 + -5x + 16x2 = 5x + -5x + -16x2 + 16x2 Combine like terms: 5x + -5x = 0 -40 + -5x + 16x2 = 0 + -16x2 + 16x2 -40 + -5x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -40 + -5x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -2.5 + -0.3125x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -0.3125x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -0.3125x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -0.3125x + x2 = 0 + 2.5 -0.3125x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -0.3125x + x2 = 2.5 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 = 2.5 + 0.0244140625 Reorder the terms: 0.0244140625 + -0.3125x + x2 = 2.5 + 0.0244140625 Combine like terms: 2.5 + 0.0244140625 = 2.5244140625 0.0244140625 + -0.3125x + x2 = 2.5244140625 Factor a perfect square on the left side: (x + -0.15625)(x + -0.15625) = 2.5244140625 Calculate the square root of the right side: 1.588840477 Break this problem into two subproblems by setting (x + -0.15625) equal to 1.588840477 and -1.588840477.Subproblem 1
x + -0.15625 = 1.588840477 Simplifying x + -0.15625 = 1.588840477 Reorder the terms: -0.15625 + x = 1.588840477 Solving -0.15625 + x = 1.588840477 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 = 1.588840477 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + x = 1.588840477 + 0.15625 x = 1.588840477 + 0.15625 Combine like terms: 1.588840477 + 0.15625 = 1.745090477 x = 1.745090477 Simplifying x = 1.745090477Subproblem 2
x + -0.15625 = -1.588840477 Simplifying x + -0.15625 = -1.588840477 Reorder the terms: -0.15625 + x = -1.588840477 Solving -0.15625 + x = -1.588840477 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 = -1.588840477 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + x = -1.588840477 + 0.15625 x = -1.588840477 + 0.15625 Combine like terms: -1.588840477 + 0.15625 = -1.432590477 x = -1.432590477 Simplifying x = -1.432590477Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.745090477, -1.432590477}
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