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Simplifying 9x2 + 9x + -25 = -2 Reorder the terms: -25 + 9x + 9x2 = -2 Solving -25 + 9x + 9x2 = -2 Solving for variable 'x'. Reorder the terms: -25 + 2 + 9x + 9x2 = -2 + 2 Combine like terms: -25 + 2 = -23 -23 + 9x + 9x2 = -2 + 2 Combine like terms: -2 + 2 = 0 -23 + 9x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.555555556 + x + x2 = 0 Move the constant term to the right: Add '2.555555556' to each side of the equation. -2.555555556 + x + 2.555555556 + x2 = 0 + 2.555555556 Reorder the terms: -2.555555556 + 2.555555556 + x + x2 = 0 + 2.555555556 Combine like terms: -2.555555556 + 2.555555556 = 0.000000000 0.000000000 + x + x2 = 0 + 2.555555556 x + x2 = 0 + 2.555555556 Combine like terms: 0 + 2.555555556 = 2.555555556 x + x2 = 2.555555556 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 = 2.555555556 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 2.555555556 + 0.25 Combine like terms: 2.555555556 + 0.25 = 2.805555556 1.25 + x2 = 2.805555556 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.805555556 Calculate the square root of the right side: 1.67497927 Break this problem into two subproblems by setting (x + 0.5) equal to 1.67497927 and -1.67497927.Subproblem 1
x + 0.5 = 1.67497927 Simplifying x + 0.5 = 1.67497927 Reorder the terms: 0.5 + x = 1.67497927 Solving 0.5 + x = 1.67497927 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 = 1.67497927 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.67497927 + -0.5 x = 1.67497927 + -0.5 Combine like terms: 1.67497927 + -0.5 = 1.17497927 x = 1.17497927 Simplifying x = 1.17497927Subproblem 2
x + 0.5 = -1.67497927 Simplifying x + 0.5 = -1.67497927 Reorder the terms: 0.5 + x = -1.67497927 Solving 0.5 + x = -1.67497927 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 = -1.67497927 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.67497927 + -0.5 x = -1.67497927 + -0.5 Combine like terms: -1.67497927 + -0.5 = -2.17497927 x = -2.17497927 Simplifying x = -2.17497927Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.17497927, -2.17497927}
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