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Simplifying 2x2 + 27x + -30 = 0 Reorder the terms: -30 + 27x + 2x2 = 0 Solving -30 + 27x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -15 + 13.5x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 13.5x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 13.5x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 13.5x + x2 = 0 + 15 13.5x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 13.5x + x2 = 15 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 = 15 + 45.5625 Reorder the terms: 45.5625 + 13.5x + x2 = 15 + 45.5625 Combine like terms: 15 + 45.5625 = 60.5625 45.5625 + 13.5x + x2 = 60.5625 Factor a perfect square on the left side: (x + 6.75)(x + 6.75) = 60.5625 Calculate the square root of the right side: 7.782191208 Break this problem into two subproblems by setting (x + 6.75) equal to 7.782191208 and -7.782191208.Subproblem 1
x + 6.75 = 7.782191208 Simplifying x + 6.75 = 7.782191208 Reorder the terms: 6.75 + x = 7.782191208 Solving 6.75 + x = 7.782191208 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 = 7.782191208 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + x = 7.782191208 + -6.75 x = 7.782191208 + -6.75 Combine like terms: 7.782191208 + -6.75 = 1.032191208 x = 1.032191208 Simplifying x = 1.032191208Subproblem 2
x + 6.75 = -7.782191208 Simplifying x + 6.75 = -7.782191208 Reorder the terms: 6.75 + x = -7.782191208 Solving 6.75 + x = -7.782191208 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 = -7.782191208 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + x = -7.782191208 + -6.75 x = -7.782191208 + -6.75 Combine like terms: -7.782191208 + -6.75 = -14.532191208 x = -14.532191208 Simplifying x = -14.532191208Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.032191208, -14.532191208}
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