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Simplifying 9x2 + -32x + -8 = 0 Reorder the terms: -8 + -32x + 9x2 = 0 Solving -8 + -32x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.8888888889 + -3.555555556x + x2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + -3.555555556x + 0.8888888889 + x2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + -3.555555556x + x2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + -3.555555556x + x2 = 0 + 0.8888888889 -3.555555556x + x2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 -3.555555556x + x2 = 0.8888888889 The x term is -3.555555556x. Take half its coefficient (-1.777777778). Square it (3.160493828) and add it to both sides. Add '3.160493828' to each side of the equation. -3.555555556x + 3.160493828 + x2 = 0.8888888889 + 3.160493828 Reorder the terms: 3.160493828 + -3.555555556x + x2 = 0.8888888889 + 3.160493828 Combine like terms: 0.8888888889 + 3.160493828 = 4.0493827169 3.160493828 + -3.555555556x + x2 = 4.0493827169 Factor a perfect square on the left side: (x + -1.777777778)(x + -1.777777778) = 4.0493827169 Calculate the square root of the right side: 2.012307809 Break this problem into two subproblems by setting (x + -1.777777778) equal to 2.012307809 and -2.012307809.Subproblem 1
x + -1.777777778 = 2.012307809 Simplifying x + -1.777777778 = 2.012307809 Reorder the terms: -1.777777778 + x = 2.012307809 Solving -1.777777778 + x = 2.012307809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.777777778' to each side of the equation. -1.777777778 + 1.777777778 + x = 2.012307809 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + x = 2.012307809 + 1.777777778 x = 2.012307809 + 1.777777778 Combine like terms: 2.012307809 + 1.777777778 = 3.790085587 x = 3.790085587 Simplifying x = 3.790085587Subproblem 2
x + -1.777777778 = -2.012307809 Simplifying x + -1.777777778 = -2.012307809 Reorder the terms: -1.777777778 + x = -2.012307809 Solving -1.777777778 + x = -2.012307809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.777777778' to each side of the equation. -1.777777778 + 1.777777778 + x = -2.012307809 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + x = -2.012307809 + 1.777777778 x = -2.012307809 + 1.777777778 Combine like terms: -2.012307809 + 1.777777778 = -0.234530031 x = -0.234530031 Simplifying x = -0.234530031Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.790085587, -0.234530031}
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