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Simplifying 18x2 + 14x + -16 = 0 Reorder the terms: -16 + 14x + 18x2 = 0 Solving -16 + 14x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 7x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + 7x + 9x2)' equal to zero and attempt to solve: Simplifying -8 + 7x + 9x2 = 0 Solving -8 + 7x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.8888888889 + 0.7777777778x + x2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + 0.7777777778x + 0.8888888889 + x2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + 0.7777777778x + x2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + 0.7777777778x + x2 = 0 + 0.8888888889 0.7777777778x + x2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 0.7777777778x + x2 = 0.8888888889 The x term is 0.7777777778x. Take half its coefficient (0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. 0.7777777778x + 0.1512345679 + x2 = 0.8888888889 + 0.1512345679 Reorder the terms: 0.1512345679 + 0.7777777778x + x2 = 0.8888888889 + 0.1512345679 Combine like terms: 0.8888888889 + 0.1512345679 = 1.0401234568 0.1512345679 + 0.7777777778x + x2 = 1.0401234568 Factor a perfect square on the left side: (x + 0.3888888889)(x + 0.3888888889) = 1.0401234568 Calculate the square root of the right side: 1.019864431 Break this problem into two subproblems by setting (x + 0.3888888889) equal to 1.019864431 and -1.019864431.Subproblem 1
x + 0.3888888889 = 1.019864431 Simplifying x + 0.3888888889 = 1.019864431 Reorder the terms: 0.3888888889 + x = 1.019864431 Solving 0.3888888889 + x = 1.019864431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3888888889' to each side of the equation. 0.3888888889 + -0.3888888889 + x = 1.019864431 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = 1.019864431 + -0.3888888889 x = 1.019864431 + -0.3888888889 Combine like terms: 1.019864431 + -0.3888888889 = 0.6309755421 x = 0.6309755421 Simplifying x = 0.6309755421Subproblem 2
x + 0.3888888889 = -1.019864431 Simplifying x + 0.3888888889 = -1.019864431 Reorder the terms: 0.3888888889 + x = -1.019864431 Solving 0.3888888889 + x = -1.019864431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3888888889' to each side of the equation. 0.3888888889 + -0.3888888889 + x = -1.019864431 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = -1.019864431 + -0.3888888889 x = -1.019864431 + -0.3888888889 Combine like terms: -1.019864431 + -0.3888888889 = -1.4087533199 x = -1.4087533199 Simplifying x = -1.4087533199Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6309755421, -1.4087533199}Solution
x = {0.6309755421, -1.4087533199}
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