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Simplifying 0 = x2 + 12x + -35 Reorder the terms: 0 = -35 + 12x + x2 Solving 0 = -35 + 12x + x2 Solving for variable 'x'. Combine like terms: 0 + 35 = 35 35 + -12x + -1x2 = -35 + 12x + x2 + 35 + -12x + -1x2 Reorder the terms: 35 + -12x + -1x2 = -35 + 35 + 12x + -12x + x2 + -1x2 Combine like terms: -35 + 35 = 0 35 + -12x + -1x2 = 0 + 12x + -12x + x2 + -1x2 35 + -12x + -1x2 = 12x + -12x + x2 + -1x2 Combine like terms: 12x + -12x = 0 35 + -12x + -1x2 = 0 + x2 + -1x2 35 + -12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 35 + -12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -35 + 12x + x2 = 0 Move the constant term to the right: Add '35' to each side of the equation. -35 + 12x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + 12x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 12x + x2 = 0 + 35 12x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 12x + x2 = 35 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 35 + 36 Reorder the terms: 36 + 12x + x2 = 35 + 36 Combine like terms: 35 + 36 = 71 36 + 12x + x2 = 71 Factor a perfect square on the left side: (x + 6)(x + 6) = 71 Calculate the square root of the right side: 8.426149773 Break this problem into two subproblems by setting (x + 6) equal to 8.426149773 and -8.426149773.Subproblem 1
x + 6 = 8.426149773 Simplifying x + 6 = 8.426149773 Reorder the terms: 6 + x = 8.426149773 Solving 6 + x = 8.426149773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 8.426149773 + -6 Combine like terms: 6 + -6 = 0 0 + x = 8.426149773 + -6 x = 8.426149773 + -6 Combine like terms: 8.426149773 + -6 = 2.426149773 x = 2.426149773 Simplifying x = 2.426149773Subproblem 2
x + 6 = -8.426149773 Simplifying x + 6 = -8.426149773 Reorder the terms: 6 + x = -8.426149773 Solving 6 + x = -8.426149773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -8.426149773 + -6 Combine like terms: 6 + -6 = 0 0 + x = -8.426149773 + -6 x = -8.426149773 + -6 Combine like terms: -8.426149773 + -6 = -14.426149773 x = -14.426149773 Simplifying x = -14.426149773Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.426149773, -14.426149773}
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