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Simplifying 0 = x2 + 8x + -54 Reorder the terms: 0 = -54 + 8x + x2 Solving 0 = -54 + 8x + x2 Solving for variable 'x'. Combine like terms: 0 + 54 = 54 54 + -8x + -1x2 = -54 + 8x + x2 + 54 + -8x + -1x2 Reorder the terms: 54 + -8x + -1x2 = -54 + 54 + 8x + -8x + x2 + -1x2 Combine like terms: -54 + 54 = 0 54 + -8x + -1x2 = 0 + 8x + -8x + x2 + -1x2 54 + -8x + -1x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 54 + -8x + -1x2 = 0 + x2 + -1x2 54 + -8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 54 + -8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -54 + 8x + x2 = 0 Move the constant term to the right: Add '54' to each side of the equation. -54 + 8x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + 8x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 8x + x2 = 0 + 54 8x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 8x + x2 = 54 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 = 54 + 16 Reorder the terms: 16 + 8x + x2 = 54 + 16 Combine like terms: 54 + 16 = 70 16 + 8x + x2 = 70 Factor a perfect square on the left side: (x + 4)(x + 4) = 70 Calculate the square root of the right side: 8.366600265 Break this problem into two subproblems by setting (x + 4) equal to 8.366600265 and -8.366600265.Subproblem 1
x + 4 = 8.366600265 Simplifying x + 4 = 8.366600265 Reorder the terms: 4 + x = 8.366600265 Solving 4 + x = 8.366600265 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 = 8.366600265 + -4 Combine like terms: 4 + -4 = 0 0 + x = 8.366600265 + -4 x = 8.366600265 + -4 Combine like terms: 8.366600265 + -4 = 4.366600265 x = 4.366600265 Simplifying x = 4.366600265Subproblem 2
x + 4 = -8.366600265 Simplifying x + 4 = -8.366600265 Reorder the terms: 4 + x = -8.366600265 Solving 4 + x = -8.366600265 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 = -8.366600265 + -4 Combine like terms: 4 + -4 = 0 0 + x = -8.366600265 + -4 x = -8.366600265 + -4 Combine like terms: -8.366600265 + -4 = -12.366600265 x = -12.366600265 Simplifying x = -12.366600265Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.366600265, -12.366600265}
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