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Simplifying 0 = -16x2 + 5x + 15 Reorder the terms: 0 = 15 + 5x + -16x2 Solving 0 = 15 + 5x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -15 = -15 -15 + -5x + 16x2 = 15 + 5x + -16x2 + -15 + -5x + 16x2 Reorder the terms: -15 + -5x + 16x2 = 15 + -15 + 5x + -5x + -16x2 + 16x2 Combine like terms: 15 + -15 = 0 -15 + -5x + 16x2 = 0 + 5x + -5x + -16x2 + 16x2 -15 + -5x + 16x2 = 5x + -5x + -16x2 + 16x2 Combine like terms: 5x + -5x = 0 -15 + -5x + 16x2 = 0 + -16x2 + 16x2 -15 + -5x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -15 + -5x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.9375 + -0.3125x + x2 = 0 Move the constant term to the right: Add '0.9375' to each side of the equation. -0.9375 + -0.3125x + 0.9375 + x2 = 0 + 0.9375 Reorder the terms: -0.9375 + 0.9375 + -0.3125x + x2 = 0 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + -0.3125x + x2 = 0 + 0.9375 -0.3125x + x2 = 0 + 0.9375 Combine like terms: 0 + 0.9375 = 0.9375 -0.3125x + x2 = 0.9375 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 = 0.9375 + 0.0244140625 Reorder the terms: 0.0244140625 + -0.3125x + x2 = 0.9375 + 0.0244140625 Combine like terms: 0.9375 + 0.0244140625 = 0.9619140625 0.0244140625 + -0.3125x + x2 = 0.9619140625 Factor a perfect square on the left side: (x + -0.15625)(x + -0.15625) = 0.9619140625 Calculate the square root of the right side: 0.980772177 Break this problem into two subproblems by setting (x + -0.15625) equal to 0.980772177 and -0.980772177.Subproblem 1
x + -0.15625 = 0.980772177 Simplifying x + -0.15625 = 0.980772177 Reorder the terms: -0.15625 + x = 0.980772177 Solving -0.15625 + x = 0.980772177 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 = 0.980772177 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + x = 0.980772177 + 0.15625 x = 0.980772177 + 0.15625 Combine like terms: 0.980772177 + 0.15625 = 1.137022177 x = 1.137022177 Simplifying x = 1.137022177Subproblem 2
x + -0.15625 = -0.980772177 Simplifying x + -0.15625 = -0.980772177 Reorder the terms: -0.15625 + x = -0.980772177 Solving -0.15625 + x = -0.980772177 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 = -0.980772177 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + x = -0.980772177 + 0.15625 x = -0.980772177 + 0.15625 Combine like terms: -0.980772177 + 0.15625 = -0.824522177 x = -0.824522177 Simplifying x = -0.824522177Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.137022177, -0.824522177}
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