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Simplifying 9x2 + 27x + 5 = 0 Reorder the terms: 5 + 27x + 9x2 = 0 Solving 5 + 27x + 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'. 0.5555555556 + 3x + x2 = 0 Move the constant term to the right: Add '-0.5555555556' to each side of the equation. 0.5555555556 + 3x + -0.5555555556 + x2 = 0 + -0.5555555556 Reorder the terms: 0.5555555556 + -0.5555555556 + 3x + x2 = 0 + -0.5555555556 Combine like terms: 0.5555555556 + -0.5555555556 = 0.0000000000 0.0000000000 + 3x + x2 = 0 + -0.5555555556 3x + x2 = 0 + -0.5555555556 Combine like terms: 0 + -0.5555555556 = -0.5555555556 3x + x2 = -0.5555555556 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -0.5555555556 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -0.5555555556 + 2.25 Combine like terms: -0.5555555556 + 2.25 = 1.6944444444 2.25 + 3x + x2 = 1.6944444444 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 1.6944444444 Calculate the square root of the right side: 1.301708279 Break this problem into two subproblems by setting (x + 1.5) equal to 1.301708279 and -1.301708279.Subproblem 1
x + 1.5 = 1.301708279 Simplifying x + 1.5 = 1.301708279 Reorder the terms: 1.5 + x = 1.301708279 Solving 1.5 + x = 1.301708279 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.301708279 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.301708279 + -1.5 x = 1.301708279 + -1.5 Combine like terms: 1.301708279 + -1.5 = -0.198291721 x = -0.198291721 Simplifying x = -0.198291721Subproblem 2
x + 1.5 = -1.301708279 Simplifying x + 1.5 = -1.301708279 Reorder the terms: 1.5 + x = -1.301708279 Solving 1.5 + x = -1.301708279 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.301708279 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.301708279 + -1.5 x = -1.301708279 + -1.5 Combine like terms: -1.301708279 + -1.5 = -2.801708279 x = -2.801708279 Simplifying x = -2.801708279Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.198291721, -2.801708279}
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