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Simplifying 72 + x(x + -2) = 180 Reorder the terms: 72 + x(-2 + x) = 180 72 + (-2 * x + x * x) = 180 72 + (-2x + x2) = 180 Solving 72 + -2x + x2 = 180 Solving for variable 'x'. Reorder the terms: 72 + -180 + -2x + x2 = 180 + -180 Combine like terms: 72 + -180 = -108 -108 + -2x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -108 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '108' to each side of the equation. -108 + -2x + 108 + x2 = 0 + 108 Reorder the terms: -108 + 108 + -2x + x2 = 0 + 108 Combine like terms: -108 + 108 = 0 0 + -2x + x2 = 0 + 108 -2x + x2 = 0 + 108 Combine like terms: 0 + 108 = 108 -2x + x2 = 108 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 108 + 1 Reorder the terms: 1 + -2x + x2 = 108 + 1 Combine like terms: 108 + 1 = 109 1 + -2x + x2 = 109 Factor a perfect square on the left side: (x + -1)(x + -1) = 109 Calculate the square root of the right side: 10.440306509 Break this problem into two subproblems by setting (x + -1) equal to 10.440306509 and -10.440306509.Subproblem 1
x + -1 = 10.440306509 Simplifying x + -1 = 10.440306509 Reorder the terms: -1 + x = 10.440306509 Solving -1 + x = 10.440306509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 10.440306509 + 1 Combine like terms: -1 + 1 = 0 0 + x = 10.440306509 + 1 x = 10.440306509 + 1 Combine like terms: 10.440306509 + 1 = 11.440306509 x = 11.440306509 Simplifying x = 11.440306509Subproblem 2
x + -1 = -10.440306509 Simplifying x + -1 = -10.440306509 Reorder the terms: -1 + x = -10.440306509 Solving -1 + x = -10.440306509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -10.440306509 + 1 Combine like terms: -1 + 1 = 0 0 + x = -10.440306509 + 1 x = -10.440306509 + 1 Combine like terms: -10.440306509 + 1 = -9.440306509 x = -9.440306509 Simplifying x = -9.440306509Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.440306509, -9.440306509}
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