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Simplifying 8x2 + -16x + -27 = 0 Reorder the terms: -27 + -16x + 8x2 = 0 Solving -27 + -16x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3.375 + -2x + x2 = 0 Move the constant term to the right: Add '3.375' to each side of the equation. -3.375 + -2x + 3.375 + x2 = 0 + 3.375 Reorder the terms: -3.375 + 3.375 + -2x + x2 = 0 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + -2x + x2 = 0 + 3.375 -2x + x2 = 0 + 3.375 Combine like terms: 0 + 3.375 = 3.375 -2x + x2 = 3.375 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 3.375 + 1 Reorder the terms: 1 + -2x + x2 = 3.375 + 1 Combine like terms: 3.375 + 1 = 4.375 1 + -2x + x2 = 4.375 Factor a perfect square on the left side: (x + -1)(x + -1) = 4.375 Calculate the square root of the right side: 2.091650066 Break this problem into two subproblems by setting (x + -1) equal to 2.091650066 and -2.091650066.Subproblem 1
x + -1 = 2.091650066 Simplifying x + -1 = 2.091650066 Reorder the terms: -1 + x = 2.091650066 Solving -1 + x = 2.091650066 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.091650066 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.091650066 + 1 x = 2.091650066 + 1 Combine like terms: 2.091650066 + 1 = 3.091650066 x = 3.091650066 Simplifying x = 3.091650066Subproblem 2
x + -1 = -2.091650066 Simplifying x + -1 = -2.091650066 Reorder the terms: -1 + x = -2.091650066 Solving -1 + x = -2.091650066 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.091650066 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.091650066 + 1 x = -2.091650066 + 1 Combine like terms: -2.091650066 + 1 = -1.091650066 x = -1.091650066 Simplifying x = -1.091650066Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.091650066, -1.091650066}
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