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Simplifying -8x + -1x2 + 63 = 0 Reorder the terms: 63 + -8x + -1x2 = 0 Solving 63 + -8x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -63 + 8x + x2 = 0 Move the constant term to the right: Add '63' to each side of the equation. -63 + 8x + 63 + x2 = 0 + 63 Reorder the terms: -63 + 63 + 8x + x2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + 8x + x2 = 0 + 63 8x + x2 = 0 + 63 Combine like terms: 0 + 63 = 63 8x + x2 = 63 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 = 63 + 16 Reorder the terms: 16 + 8x + x2 = 63 + 16 Combine like terms: 63 + 16 = 79 16 + 8x + x2 = 79 Factor a perfect square on the left side: (x + 4)(x + 4) = 79 Calculate the square root of the right side: 8.888194417 Break this problem into two subproblems by setting (x + 4) equal to 8.888194417 and -8.888194417.Subproblem 1
x + 4 = 8.888194417 Simplifying x + 4 = 8.888194417 Reorder the terms: 4 + x = 8.888194417 Solving 4 + x = 8.888194417 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 = 8.888194417 + -4 Combine like terms: 4 + -4 = 0 0 + x = 8.888194417 + -4 x = 8.888194417 + -4 Combine like terms: 8.888194417 + -4 = 4.888194417 x = 4.888194417 Simplifying x = 4.888194417Subproblem 2
x + 4 = -8.888194417 Simplifying x + 4 = -8.888194417 Reorder the terms: 4 + x = -8.888194417 Solving 4 + x = -8.888194417 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 = -8.888194417 + -4 Combine like terms: 4 + -4 = 0 0 + x = -8.888194417 + -4 x = -8.888194417 + -4 Combine like terms: -8.888194417 + -4 = -12.888194417 x = -12.888194417 Simplifying x = -12.888194417Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.888194417, -12.888194417}
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