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Simplifying -1x2 + 8x = -27 Reorder the terms: 8x + -1x2 = -27 Solving 8x + -1x2 = -27 Solving for variable 'x'. Reorder the terms: 27 + 8x + -1x2 = -27 + 27 Combine like terms: -27 + 27 = 0 27 + 8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -27 + -8x + x2 = 0 Move the constant term to the right: Add '27' to each side of the equation. -27 + -8x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + -8x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -8x + x2 = 0 + 27 -8x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 -8x + x2 = 27 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 = 27 + 16 Reorder the terms: 16 + -8x + x2 = 27 + 16 Combine like terms: 27 + 16 = 43 16 + -8x + x2 = 43 Factor a perfect square on the left side: (x + -4)(x + -4) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (x + -4) equal to 6.557438524 and -6.557438524.Subproblem 1
x + -4 = 6.557438524 Simplifying x + -4 = 6.557438524 Reorder the terms: -4 + x = 6.557438524 Solving -4 + x = 6.557438524 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 = 6.557438524 + 4 Combine like terms: -4 + 4 = 0 0 + x = 6.557438524 + 4 x = 6.557438524 + 4 Combine like terms: 6.557438524 + 4 = 10.557438524 x = 10.557438524 Simplifying x = 10.557438524Subproblem 2
x + -4 = -6.557438524 Simplifying x + -4 = -6.557438524 Reorder the terms: -4 + x = -6.557438524 Solving -4 + x = -6.557438524 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 = -6.557438524 + 4 Combine like terms: -4 + 4 = 0 0 + x = -6.557438524 + 4 x = -6.557438524 + 4 Combine like terms: -6.557438524 + 4 = -2.557438524 x = -2.557438524 Simplifying x = -2.557438524Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.557438524, -2.557438524}
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