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Simplifying 0 = -16x2 + 12 + -4x + 3 Reorder the terms: 0 = 12 + 3 + -4x + -16x2 Combine like terms: 12 + 3 = 15 0 = 15 + -4x + -16x2 Solving 0 = 15 + -4x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -15 = -15 -15 + 4x + 16x2 = 15 + -4x + -16x2 + -15 + 4x + 16x2 Reorder the terms: -15 + 4x + 16x2 = 15 + -15 + -4x + 4x + -16x2 + 16x2 Combine like terms: 15 + -15 = 0 -15 + 4x + 16x2 = 0 + -4x + 4x + -16x2 + 16x2 -15 + 4x + 16x2 = -4x + 4x + -16x2 + 16x2 Combine like terms: -4x + 4x = 0 -15 + 4x + 16x2 = 0 + -16x2 + 16x2 -15 + 4x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -15 + 4x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.9375 + 0.25x + x2 = 0 Move the constant term to the right: Add '0.9375' to each side of the equation. -0.9375 + 0.25x + 0.9375 + x2 = 0 + 0.9375 Reorder the terms: -0.9375 + 0.9375 + 0.25x + x2 = 0 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + 0.25x + x2 = 0 + 0.9375 0.25x + x2 = 0 + 0.9375 Combine like terms: 0 + 0.9375 = 0.9375 0.25x + x2 = 0.9375 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = 0.9375 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 0.9375 + 0.015625 Combine like terms: 0.9375 + 0.015625 = 0.953125 0.015625 + 0.25x + x2 = 0.953125 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 0.953125 Calculate the square root of the right side: 0.976281209 Break this problem into two subproblems by setting (x + 0.125) equal to 0.976281209 and -0.976281209.Subproblem 1
x + 0.125 = 0.976281209 Simplifying x + 0.125 = 0.976281209 Reorder the terms: 0.125 + x = 0.976281209 Solving 0.125 + x = 0.976281209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 0.976281209 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 0.976281209 + -0.125 x = 0.976281209 + -0.125 Combine like terms: 0.976281209 + -0.125 = 0.851281209 x = 0.851281209 Simplifying x = 0.851281209Subproblem 2
x + 0.125 = -0.976281209 Simplifying x + 0.125 = -0.976281209 Reorder the terms: 0.125 + x = -0.976281209 Solving 0.125 + x = -0.976281209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -0.976281209 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -0.976281209 + -0.125 x = -0.976281209 + -0.125 Combine like terms: -0.976281209 + -0.125 = -1.101281209 x = -1.101281209 Simplifying x = -1.101281209Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.851281209, -1.101281209}
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