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Simplifying 0 = x2 + 6x + -76 Reorder the terms: 0 = -76 + 6x + x2 Solving 0 = -76 + 6x + x2 Solving for variable 'x'. Combine like terms: 0 + 76 = 76 76 + -6x + -1x2 = -76 + 6x + x2 + 76 + -6x + -1x2 Reorder the terms: 76 + -6x + -1x2 = -76 + 76 + 6x + -6x + x2 + -1x2 Combine like terms: -76 + 76 = 0 76 + -6x + -1x2 = 0 + 6x + -6x + x2 + -1x2 76 + -6x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 76 + -6x + -1x2 = 0 + x2 + -1x2 76 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 76 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -76 + 6x + x2 = 0 Move the constant term to the right: Add '76' to each side of the equation. -76 + 6x + 76 + x2 = 0 + 76 Reorder the terms: -76 + 76 + 6x + x2 = 0 + 76 Combine like terms: -76 + 76 = 0 0 + 6x + x2 = 0 + 76 6x + x2 = 0 + 76 Combine like terms: 0 + 76 = 76 6x + x2 = 76 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 = 76 + 9 Reorder the terms: 9 + 6x + x2 = 76 + 9 Combine like terms: 76 + 9 = 85 9 + 6x + x2 = 85 Factor a perfect square on the left side: (x + 3)(x + 3) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (x + 3) equal to 9.219544457 and -9.219544457.Subproblem 1
x + 3 = 9.219544457 Simplifying x + 3 = 9.219544457 Reorder the terms: 3 + x = 9.219544457 Solving 3 + x = 9.219544457 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 = 9.219544457 + -3 Combine like terms: 3 + -3 = 0 0 + x = 9.219544457 + -3 x = 9.219544457 + -3 Combine like terms: 9.219544457 + -3 = 6.219544457 x = 6.219544457 Simplifying x = 6.219544457Subproblem 2
x + 3 = -9.219544457 Simplifying x + 3 = -9.219544457 Reorder the terms: 3 + x = -9.219544457 Solving 3 + x = -9.219544457 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 = -9.219544457 + -3 Combine like terms: 3 + -3 = 0 0 + x = -9.219544457 + -3 x = -9.219544457 + -3 Combine like terms: -9.219544457 + -3 = -12.219544457 x = -12.219544457 Simplifying x = -12.219544457Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.219544457, -12.219544457}
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