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Simplifying 9x2 + 9x + -14 = 0 Reorder the terms: -14 + 9x + 9x2 = 0 Solving -14 + 9x + 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'. -1.555555556 + x + x2 = 0 Move the constant term to the right: Add '1.555555556' to each side of the equation. -1.555555556 + x + 1.555555556 + x2 = 0 + 1.555555556 Reorder the terms: -1.555555556 + 1.555555556 + x + x2 = 0 + 1.555555556 Combine like terms: -1.555555556 + 1.555555556 = 0.000000000 0.000000000 + x + x2 = 0 + 1.555555556 x + x2 = 0 + 1.555555556 Combine like terms: 0 + 1.555555556 = 1.555555556 x + x2 = 1.555555556 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 1.555555556 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 1.555555556 + 0.25 Combine like terms: 1.555555556 + 0.25 = 1.805555556 1.25 + x2 = 1.805555556 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1.805555556 Calculate the square root of the right side: 1.343709625 Break this problem into two subproblems by setting (x + 0.5) equal to 1.343709625 and -1.343709625.Subproblem 1
x + 0.5 = 1.343709625 Simplifying x + 0.5 = 1.343709625 Reorder the terms: 0.5 + x = 1.343709625 Solving 0.5 + x = 1.343709625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.343709625 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.343709625 + -0.5 x = 1.343709625 + -0.5 Combine like terms: 1.343709625 + -0.5 = 0.843709625 x = 0.843709625 Simplifying x = 0.843709625Subproblem 2
x + 0.5 = -1.343709625 Simplifying x + 0.5 = -1.343709625 Reorder the terms: 0.5 + x = -1.343709625 Solving 0.5 + x = -1.343709625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.343709625 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.343709625 + -0.5 x = -1.343709625 + -0.5 Combine like terms: -1.343709625 + -0.5 = -1.843709625 x = -1.843709625 Simplifying x = -1.843709625Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.843709625, -1.843709625}
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