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Simplifying 16x2 + 20x + -9 = 0 Reorder the terms: -9 + 20x + 16x2 = 0 Solving -9 + 20x + 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'. -0.5625 + 1.25x + x2 = 0 Move the constant term to the right: Add '0.5625' to each side of the equation. -0.5625 + 1.25x + 0.5625 + x2 = 0 + 0.5625 Reorder the terms: -0.5625 + 0.5625 + 1.25x + x2 = 0 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + 1.25x + x2 = 0 + 0.5625 1.25x + x2 = 0 + 0.5625 Combine like terms: 0 + 0.5625 = 0.5625 1.25x + x2 = 0.5625 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 0.5625 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 0.5625 + 0.390625 Combine like terms: 0.5625 + 0.390625 = 0.953125 0.390625 + 1.25x + x2 = 0.953125 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 0.953125 Calculate the square root of the right side: 0.976281209 Break this problem into two subproblems by setting (x + 0.625) equal to 0.976281209 and -0.976281209.Subproblem 1
x + 0.625 = 0.976281209 Simplifying x + 0.625 = 0.976281209 Reorder the terms: 0.625 + x = 0.976281209 Solving 0.625 + x = 0.976281209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 0.976281209 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 0.976281209 + -0.625 x = 0.976281209 + -0.625 Combine like terms: 0.976281209 + -0.625 = 0.351281209 x = 0.351281209 Simplifying x = 0.351281209Subproblem 2
x + 0.625 = -0.976281209 Simplifying x + 0.625 = -0.976281209 Reorder the terms: 0.625 + x = -0.976281209 Solving 0.625 + x = -0.976281209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -0.976281209 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -0.976281209 + -0.625 x = -0.976281209 + -0.625 Combine like terms: -0.976281209 + -0.625 = -1.601281209 x = -1.601281209 Simplifying x = -1.601281209Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.351281209, -1.601281209}
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