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Simplifying (x)(2x + -9) = 27 Reorder the terms: x(-9 + 2x) = 27 (-9 * x + 2x * x) = 27 (-9x + 2x2) = 27 Solving -9x + 2x2 = 27 Solving for variable 'x'. Reorder the terms: -27 + -9x + 2x2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + -9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -13.5 + -4.5x + x2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + -4.5x + 13.5 + x2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + -4.5x + x2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + -4.5x + x2 = 0 + 13.5 -4.5x + x2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 -4.5x + x2 = 13.5 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 13.5 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 13.5 + 5.0625 Combine like terms: 13.5 + 5.0625 = 18.5625 5.0625 + -4.5x + x2 = 18.5625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 18.5625 Calculate the square root of the right side: 4.308421985 Break this problem into two subproblems by setting (x + -2.25) equal to 4.308421985 and -4.308421985.Subproblem 1
x + -2.25 = 4.308421985 Simplifying x + -2.25 = 4.308421985 Reorder the terms: -2.25 + x = 4.308421985 Solving -2.25 + x = 4.308421985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 4.308421985 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 4.308421985 + 2.25 x = 4.308421985 + 2.25 Combine like terms: 4.308421985 + 2.25 = 6.558421985 x = 6.558421985 Simplifying x = 6.558421985Subproblem 2
x + -2.25 = -4.308421985 Simplifying x + -2.25 = -4.308421985 Reorder the terms: -2.25 + x = -4.308421985 Solving -2.25 + x = -4.308421985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -4.308421985 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -4.308421985 + 2.25 x = -4.308421985 + 2.25 Combine like terms: -4.308421985 + 2.25 = -2.058421985 x = -2.058421985 Simplifying x = -2.058421985Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.558421985, -2.058421985}
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