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Simplifying 13 = -9x2 + -27x Reorder the terms: 13 = -27x + -9x2 Solving 13 = -27x + -9x2 Solving for variable 'x'. Reorder the terms: 13 + 27x + 9x2 = -27x + 27x + -9x2 + 9x2 Combine like terms: -27x + 27x = 0 13 + 27x + 9x2 = 0 + -9x2 + 9x2 13 + 27x + 9x2 = -9x2 + 9x2 Combine like terms: -9x2 + 9x2 = 0 13 + 27x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1.444444444 + 3x + x2 = 0 Move the constant term to the right: Add '-1.444444444' to each side of the equation. 1.444444444 + 3x + -1.444444444 + x2 = 0 + -1.444444444 Reorder the terms: 1.444444444 + -1.444444444 + 3x + x2 = 0 + -1.444444444 Combine like terms: 1.444444444 + -1.444444444 = 0.000000000 0.000000000 + 3x + x2 = 0 + -1.444444444 3x + x2 = 0 + -1.444444444 Combine like terms: 0 + -1.444444444 = -1.444444444 3x + x2 = -1.444444444 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 = -1.444444444 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -1.444444444 + 2.25 Combine like terms: -1.444444444 + 2.25 = 0.805555556 2.25 + 3x + x2 = 0.805555556 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 0.805555556 Calculate the square root of the right side: 0.897527468 Break this problem into two subproblems by setting (x + 1.5) equal to 0.897527468 and -0.897527468.Subproblem 1
x + 1.5 = 0.897527468 Simplifying x + 1.5 = 0.897527468 Reorder the terms: 1.5 + x = 0.897527468 Solving 1.5 + x = 0.897527468 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 = 0.897527468 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 0.897527468 + -1.5 x = 0.897527468 + -1.5 Combine like terms: 0.897527468 + -1.5 = -0.602472532 x = -0.602472532 Simplifying x = -0.602472532Subproblem 2
x + 1.5 = -0.897527468 Simplifying x + 1.5 = -0.897527468 Reorder the terms: 1.5 + x = -0.897527468 Solving 1.5 + x = -0.897527468 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 = -0.897527468 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -0.897527468 + -1.5 x = -0.897527468 + -1.5 Combine like terms: -0.897527468 + -1.5 = -2.397527468 x = -2.397527468 Simplifying x = -2.397527468Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.602472532, -2.397527468}
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