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Simplifying 2x2 + 27x = 7 Reorder the terms: 27x + 2x2 = 7 Solving 27x + 2x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + 27x + 2x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 27x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + 13.5x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 13.5x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 13.5x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 13.5x + x2 = 0 + 3.5 13.5x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 13.5x + x2 = 3.5 The x term is 13.5x. Take half its coefficient (6.75). Square it (45.5625) and add it to both sides. Add '45.5625' to each side of the equation. 13.5x + 45.5625 + x2 = 3.5 + 45.5625 Reorder the terms: 45.5625 + 13.5x + x2 = 3.5 + 45.5625 Combine like terms: 3.5 + 45.5625 = 49.0625 45.5625 + 13.5x + x2 = 49.0625 Factor a perfect square on the left side: (x + 6.75)(x + 6.75) = 49.0625 Calculate the square root of the right side: 7.004462863 Break this problem into two subproblems by setting (x + 6.75) equal to 7.004462863 and -7.004462863.Subproblem 1
x + 6.75 = 7.004462863 Simplifying x + 6.75 = 7.004462863 Reorder the terms: 6.75 + x = 7.004462863 Solving 6.75 + x = 7.004462863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.75' to each side of the equation. 6.75 + -6.75 + x = 7.004462863 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + x = 7.004462863 + -6.75 x = 7.004462863 + -6.75 Combine like terms: 7.004462863 + -6.75 = 0.254462863 x = 0.254462863 Simplifying x = 0.254462863Subproblem 2
x + 6.75 = -7.004462863 Simplifying x + 6.75 = -7.004462863 Reorder the terms: 6.75 + x = -7.004462863 Solving 6.75 + x = -7.004462863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.75' to each side of the equation. 6.75 + -6.75 + x = -7.004462863 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + x = -7.004462863 + -6.75 x = -7.004462863 + -6.75 Combine like terms: -7.004462863 + -6.75 = -13.754462863 x = -13.754462863 Simplifying x = -13.754462863Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.254462863, -13.754462863}
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