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Simplifying 2x2 + -16x + -27 = 0 Reorder the terms: -27 + -16x + 2x2 = 0 Solving -27 + -16x + 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'. -13.5 + -8x + x2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + -8x + 13.5 + x2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + -8x + x2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + -8x + x2 = 0 + 13.5 -8x + x2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 -8x + x2 = 13.5 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 13.5 + 16 Reorder the terms: 16 + -8x + x2 = 13.5 + 16 Combine like terms: 13.5 + 16 = 29.5 16 + -8x + x2 = 29.5 Factor a perfect square on the left side: (x + -4)(x + -4) = 29.5 Calculate the square root of the right side: 5.431390246 Break this problem into two subproblems by setting (x + -4) equal to 5.431390246 and -5.431390246.Subproblem 1
x + -4 = 5.431390246 Simplifying x + -4 = 5.431390246 Reorder the terms: -4 + x = 5.431390246 Solving -4 + x = 5.431390246 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 5.431390246 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.431390246 + 4 x = 5.431390246 + 4 Combine like terms: 5.431390246 + 4 = 9.431390246 x = 9.431390246 Simplifying x = 9.431390246Subproblem 2
x + -4 = -5.431390246 Simplifying x + -4 = -5.431390246 Reorder the terms: -4 + x = -5.431390246 Solving -4 + x = -5.431390246 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -5.431390246 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.431390246 + 4 x = -5.431390246 + 4 Combine like terms: -5.431390246 + 4 = -1.431390246 x = -1.431390246 Simplifying x = -1.431390246Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.431390246, -1.431390246}
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