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Simplifying 0 = x2 + 8x + -47 Reorder the terms: 0 = -47 + 8x + x2 Solving 0 = -47 + 8x + x2 Solving for variable 'x'. Combine like terms: 0 + 47 = 47 47 + -8x + -1x2 = -47 + 8x + x2 + 47 + -8x + -1x2 Reorder the terms: 47 + -8x + -1x2 = -47 + 47 + 8x + -8x + x2 + -1x2 Combine like terms: -47 + 47 = 0 47 + -8x + -1x2 = 0 + 8x + -8x + x2 + -1x2 47 + -8x + -1x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 47 + -8x + -1x2 = 0 + x2 + -1x2 47 + -8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 47 + -8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -47 + 8x + x2 = 0 Move the constant term to the right: Add '47' to each side of the equation. -47 + 8x + 47 + x2 = 0 + 47 Reorder the terms: -47 + 47 + 8x + x2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + 8x + x2 = 0 + 47 8x + x2 = 0 + 47 Combine like terms: 0 + 47 = 47 8x + x2 = 47 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 = 47 + 16 Reorder the terms: 16 + 8x + x2 = 47 + 16 Combine like terms: 47 + 16 = 63 16 + 8x + x2 = 63 Factor a perfect square on the left side: (x + 4)(x + 4) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (x + 4) equal to 7.937253933 and -7.937253933.Subproblem 1
x + 4 = 7.937253933 Simplifying x + 4 = 7.937253933 Reorder the terms: 4 + x = 7.937253933 Solving 4 + x = 7.937253933 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 = 7.937253933 + -4 Combine like terms: 4 + -4 = 0 0 + x = 7.937253933 + -4 x = 7.937253933 + -4 Combine like terms: 7.937253933 + -4 = 3.937253933 x = 3.937253933 Simplifying x = 3.937253933Subproblem 2
x + 4 = -7.937253933 Simplifying x + 4 = -7.937253933 Reorder the terms: 4 + x = -7.937253933 Solving 4 + x = -7.937253933 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 = -7.937253933 + -4 Combine like terms: 4 + -4 = 0 0 + x = -7.937253933 + -4 x = -7.937253933 + -4 Combine like terms: -7.937253933 + -4 = -11.937253933 x = -11.937253933 Simplifying x = -11.937253933Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.937253933, -11.937253933}
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