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Simplifying 9x2 + 32x + -15 = 0 Reorder the terms: -15 + 32x + 9x2 = 0 Solving -15 + 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'. -1.666666667 + 3.555555556x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + 3.555555556x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + 3.555555556x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + 3.555555556x + x2 = 0 + 1.666666667 3.555555556x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 3.555555556x + x2 = 1.666666667 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 = 1.666666667 + 3.160493828 Reorder the terms: 3.160493828 + 3.555555556x + x2 = 1.666666667 + 3.160493828 Combine like terms: 1.666666667 + 3.160493828 = 4.827160495 3.160493828 + 3.555555556x + x2 = 4.827160495 Factor a perfect square on the left side: (x + 1.777777778)(x + 1.777777778) = 4.827160495 Calculate the square root of the right side: 2.197079993 Break this problem into two subproblems by setting (x + 1.777777778) equal to 2.197079993 and -2.197079993.Subproblem 1
x + 1.777777778 = 2.197079993 Simplifying x + 1.777777778 = 2.197079993 Reorder the terms: 1.777777778 + x = 2.197079993 Solving 1.777777778 + x = 2.197079993 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 = 2.197079993 + -1.777777778 Combine like terms: 1.777777778 + -1.777777778 = 0.000000000 0.000000000 + x = 2.197079993 + -1.777777778 x = 2.197079993 + -1.777777778 Combine like terms: 2.197079993 + -1.777777778 = 0.419302215 x = 0.419302215 Simplifying x = 0.419302215Subproblem 2
x + 1.777777778 = -2.197079993 Simplifying x + 1.777777778 = -2.197079993 Reorder the terms: 1.777777778 + x = -2.197079993 Solving 1.777777778 + x = -2.197079993 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 = -2.197079993 + -1.777777778 Combine like terms: 1.777777778 + -1.777777778 = 0.000000000 0.000000000 + x = -2.197079993 + -1.777777778 x = -2.197079993 + -1.777777778 Combine like terms: -2.197079993 + -1.777777778 = -3.974857771 x = -3.974857771 Simplifying x = -3.974857771Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.419302215, -3.974857771}
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