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Simplifying 176 = (x + 9)(x + -3) Reorder the terms: 176 = (9 + x)(x + -3) Reorder the terms: 176 = (9 + x)(-3 + x) Multiply (9 + x) * (-3 + x) 176 = (9(-3 + x) + x(-3 + x)) 176 = ((-3 * 9 + x * 9) + x(-3 + x)) 176 = ((-27 + 9x) + x(-3 + x)) 176 = (-27 + 9x + (-3 * x + x * x)) 176 = (-27 + 9x + (-3x + x2)) Combine like terms: 9x + -3x = 6x 176 = (-27 + 6x + x2) Solving 176 = -27 + 6x + x2 Solving for variable 'x'. Combine like terms: 176 + 27 = 203 203 + -6x + -1x2 = -27 + 6x + x2 + 27 + -6x + -1x2 Reorder the terms: 203 + -6x + -1x2 = -27 + 27 + 6x + -6x + x2 + -1x2 Combine like terms: -27 + 27 = 0 203 + -6x + -1x2 = 0 + 6x + -6x + x2 + -1x2 203 + -6x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 203 + -6x + -1x2 = 0 + x2 + -1x2 203 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 203 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -203 + 6x + x2 = 0 Move the constant term to the right: Add '203' to each side of the equation. -203 + 6x + 203 + x2 = 0 + 203 Reorder the terms: -203 + 203 + 6x + x2 = 0 + 203 Combine like terms: -203 + 203 = 0 0 + 6x + x2 = 0 + 203 6x + x2 = 0 + 203 Combine like terms: 0 + 203 = 203 6x + x2 = 203 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 = 203 + 9 Reorder the terms: 9 + 6x + x2 = 203 + 9 Combine like terms: 203 + 9 = 212 9 + 6x + x2 = 212 Factor a perfect square on the left side: (x + 3)(x + 3) = 212 Calculate the square root of the right side: 14.560219779 Break this problem into two subproblems by setting (x + 3) equal to 14.560219779 and -14.560219779.Subproblem 1
x + 3 = 14.560219779 Simplifying x + 3 = 14.560219779 Reorder the terms: 3 + x = 14.560219779 Solving 3 + x = 14.560219779 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 = 14.560219779 + -3 Combine like terms: 3 + -3 = 0 0 + x = 14.560219779 + -3 x = 14.560219779 + -3 Combine like terms: 14.560219779 + -3 = 11.560219779 x = 11.560219779 Simplifying x = 11.560219779Subproblem 2
x + 3 = -14.560219779 Simplifying x + 3 = -14.560219779 Reorder the terms: 3 + x = -14.560219779 Solving 3 + x = -14.560219779 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 = -14.560219779 + -3 Combine like terms: 3 + -3 = 0 0 + x = -14.560219779 + -3 x = -14.560219779 + -3 Combine like terms: -14.560219779 + -3 = -17.560219779 x = -17.560219779 Simplifying x = -17.560219779Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.560219779, -17.560219779}
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