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Simplifying 9x(4x + -5) + -8 = 0 Reorder the terms: 9x(-5 + 4x) + -8 = 0 (-5 * 9x + 4x * 9x) + -8 = 0 (-45x + 36x2) + -8 = 0 Reorder the terms: -8 + -45x + 36x2 = 0 Solving -8 + -45x + 36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.2222222222 + -1.25x + x2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + -1.25x + 0.2222222222 + x2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + -1.25x + x2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + -1.25x + x2 = 0 + 0.2222222222 -1.25x + x2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 -1.25x + x2 = 0.2222222222 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 = 0.2222222222 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 0.2222222222 + 0.390625 Combine like terms: 0.2222222222 + 0.390625 = 0.6128472222 0.390625 + -1.25x + x2 = 0.6128472222 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 0.6128472222 Calculate the square root of the right side: 0.782845593 Break this problem into two subproblems by setting (x + -0.625) equal to 0.782845593 and -0.782845593.Subproblem 1
x + -0.625 = 0.782845593 Simplifying x + -0.625 = 0.782845593 Reorder the terms: -0.625 + x = 0.782845593 Solving -0.625 + x = 0.782845593 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 = 0.782845593 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 0.782845593 + 0.625 x = 0.782845593 + 0.625 Combine like terms: 0.782845593 + 0.625 = 1.407845593 x = 1.407845593 Simplifying x = 1.407845593Subproblem 2
x + -0.625 = -0.782845593 Simplifying x + -0.625 = -0.782845593 Reorder the terms: -0.625 + x = -0.782845593 Solving -0.625 + x = -0.782845593 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 = -0.782845593 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -0.782845593 + 0.625 x = -0.782845593 + 0.625 Combine like terms: -0.782845593 + 0.625 = -0.157845593 x = -0.157845593 Simplifying x = -0.157845593Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.407845593, -0.157845593}
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