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Simplifying -9x2 + -18x + -2 = 0 Reorder the terms: -2 + -18x + -9x2 = 0 Solving -2 + -18x + -9x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 18x + 9x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 18x + 9x2)' equal to zero and attempt to solve: Simplifying 2 + 18x + 9x2 = 0 Solving 2 + 18x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.2222222222 + 2x + x2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + 2x + -0.2222222222 + x2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + 2x + x2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + 2x + x2 = 0 + -0.2222222222 2x + x2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 2x + x2 = -0.2222222222 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -0.2222222222 + 1 Reorder the terms: 1 + 2x + x2 = -0.2222222222 + 1 Combine like terms: -0.2222222222 + 1 = 0.7777777778 1 + 2x + x2 = 0.7777777778 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.7777777778 Calculate the square root of the right side: 0.881917104 Break this problem into two subproblems by setting (x + 1) equal to 0.881917104 and -0.881917104.Subproblem 1
x + 1 = 0.881917104 Simplifying x + 1 = 0.881917104 Reorder the terms: 1 + x = 0.881917104 Solving 1 + x = 0.881917104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.881917104 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.881917104 + -1 x = 0.881917104 + -1 Combine like terms: 0.881917104 + -1 = -0.118082896 x = -0.118082896 Simplifying x = -0.118082896Subproblem 2
x + 1 = -0.881917104 Simplifying x + 1 = -0.881917104 Reorder the terms: 1 + x = -0.881917104 Solving 1 + x = -0.881917104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.881917104 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.881917104 + -1 x = -0.881917104 + -1 Combine like terms: -0.881917104 + -1 = -1.881917104 x = -1.881917104 Simplifying x = -1.881917104Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.118082896, -1.881917104}Solution
x = {-0.118082896, -1.881917104}
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