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Simplifying 9x2 + -32x + -17 = 0 Reorder the terms: -17 + -32x + 9x2 = 0 Solving -17 + -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'. -1.888888889 + -3.555555556x + x2 = 0 Move the constant term to the right: Add '1.888888889' to each side of the equation. -1.888888889 + -3.555555556x + 1.888888889 + x2 = 0 + 1.888888889 Reorder the terms: -1.888888889 + 1.888888889 + -3.555555556x + x2 = 0 + 1.888888889 Combine like terms: -1.888888889 + 1.888888889 = 0.000000000 0.000000000 + -3.555555556x + x2 = 0 + 1.888888889 -3.555555556x + x2 = 0 + 1.888888889 Combine like terms: 0 + 1.888888889 = 1.888888889 -3.555555556x + x2 = 1.888888889 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 = 1.888888889 + 3.160493828 Reorder the terms: 3.160493828 + -3.555555556x + x2 = 1.888888889 + 3.160493828 Combine like terms: 1.888888889 + 3.160493828 = 5.049382717 3.160493828 + -3.555555556x + x2 = 5.049382717 Factor a perfect square on the left side: (x + -1.777777778)(x + -1.777777778) = 5.049382717 Calculate the square root of the right side: 2.247083158 Break this problem into two subproblems by setting (x + -1.777777778) equal to 2.247083158 and -2.247083158.Subproblem 1
x + -1.777777778 = 2.247083158 Simplifying x + -1.777777778 = 2.247083158 Reorder the terms: -1.777777778 + x = 2.247083158 Solving -1.777777778 + x = 2.247083158 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 = 2.247083158 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + x = 2.247083158 + 1.777777778 x = 2.247083158 + 1.777777778 Combine like terms: 2.247083158 + 1.777777778 = 4.024860936 x = 4.024860936 Simplifying x = 4.024860936Subproblem 2
x + -1.777777778 = -2.247083158 Simplifying x + -1.777777778 = -2.247083158 Reorder the terms: -1.777777778 + x = -2.247083158 Solving -1.777777778 + x = -2.247083158 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 = -2.247083158 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + x = -2.247083158 + 1.777777778 x = -2.247083158 + 1.777777778 Combine like terms: -2.247083158 + 1.777777778 = -0.46930538 x = -0.46930538 Simplifying x = -0.46930538Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.024860936, -0.46930538}
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