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Simplifying -8 = -37 + 6x + x2 Solving -8 = -37 + 6x + x2 Solving for variable 'x'. Combine like terms: -8 + 37 = 29 29 + -6x + -1x2 = -37 + 6x + x2 + 37 + -6x + -1x2 Reorder the terms: 29 + -6x + -1x2 = -37 + 37 + 6x + -6x + x2 + -1x2 Combine like terms: -37 + 37 = 0 29 + -6x + -1x2 = 0 + 6x + -6x + x2 + -1x2 29 + -6x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 29 + -6x + -1x2 = 0 + x2 + -1x2 29 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 29 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -29 + 6x + x2 = 0 Move the constant term to the right: Add '29' to each side of the equation. -29 + 6x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + 6x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 6x + x2 = 0 + 29 6x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 6x + x2 = 29 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 29 + 9 Reorder the terms: 9 + 6x + x2 = 29 + 9 Combine like terms: 29 + 9 = 38 9 + 6x + x2 = 38 Factor a perfect square on the left side: (x + 3)(x + 3) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (x + 3) equal to 6.164414003 and -6.164414003.Subproblem 1
x + 3 = 6.164414003 Simplifying x + 3 = 6.164414003 Reorder the terms: 3 + x = 6.164414003 Solving 3 + x = 6.164414003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 6.164414003 + -3 Combine like terms: 3 + -3 = 0 0 + x = 6.164414003 + -3 x = 6.164414003 + -3 Combine like terms: 6.164414003 + -3 = 3.164414003 x = 3.164414003 Simplifying x = 3.164414003Subproblem 2
x + 3 = -6.164414003 Simplifying x + 3 = -6.164414003 Reorder the terms: 3 + x = -6.164414003 Solving 3 + x = -6.164414003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -6.164414003 + -3 Combine like terms: 3 + -3 = 0 0 + x = -6.164414003 + -3 x = -6.164414003 + -3 Combine like terms: -6.164414003 + -3 = -9.164414003 x = -9.164414003 Simplifying x = -9.164414003Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.164414003, -9.164414003}
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