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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 = 2.5 16 + -8x + x2 = 2.5 Factor a perfect square on the left side: (x + -4)(x + -4) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting (x + -4) equal to 1.58113883 and -1.58113883.Subproblem 1
x + -4 = 1.58113883 Simplifying x + -4 = 1.58113883 Reorder the terms: -4 + x = 1.58113883 Solving -4 + x = 1.58113883 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 = 1.58113883 + 4 Combine like terms: -4 + 4 = 0 0 + x = 1.58113883 + 4 x = 1.58113883 + 4 Combine like terms: 1.58113883 + 4 = 5.58113883 x = 5.58113883 Simplifying x = 5.58113883Subproblem 2
x + -4 = -1.58113883 Simplifying x + -4 = -1.58113883 Reorder the terms: -4 + x = -1.58113883 Solving -4 + x = -1.58113883 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 = -1.58113883 + 4 Combine like terms: -4 + 4 = 0 0 + x = -1.58113883 + 4 x = -1.58113883 + 4 Combine like terms: -1.58113883 + 4 = 2.41886117 x = 2.41886117 Simplifying x = 2.41886117Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.58113883, 2.41886117}
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