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Simplifying 47 + -2x + x2 + 32 = 180 Reorder the terms: 47 + 32 + -2x + x2 = 180 Combine like terms: 47 + 32 = 79 79 + -2x + x2 = 180 Solving 79 + -2x + x2 = 180 Solving for variable 'x'. Reorder the terms: 79 + -180 + -2x + x2 = 180 + -180 Combine like terms: 79 + -180 = -101 -101 + -2x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -101 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '101' to each side of the equation. -101 + -2x + 101 + x2 = 0 + 101 Reorder the terms: -101 + 101 + -2x + x2 = 0 + 101 Combine like terms: -101 + 101 = 0 0 + -2x + x2 = 0 + 101 -2x + x2 = 0 + 101 Combine like terms: 0 + 101 = 101 -2x + x2 = 101 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 = 101 + 1 Reorder the terms: 1 + -2x + x2 = 101 + 1 Combine like terms: 101 + 1 = 102 1 + -2x + x2 = 102 Factor a perfect square on the left side: (x + -1)(x + -1) = 102 Calculate the square root of the right side: 10.099504938 Break this problem into two subproblems by setting (x + -1) equal to 10.099504938 and -10.099504938.Subproblem 1
x + -1 = 10.099504938 Simplifying x + -1 = 10.099504938 Reorder the terms: -1 + x = 10.099504938 Solving -1 + x = 10.099504938 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 = 10.099504938 + 1 Combine like terms: -1 + 1 = 0 0 + x = 10.099504938 + 1 x = 10.099504938 + 1 Combine like terms: 10.099504938 + 1 = 11.099504938 x = 11.099504938 Simplifying x = 11.099504938Subproblem 2
x + -1 = -10.099504938 Simplifying x + -1 = -10.099504938 Reorder the terms: -1 + x = -10.099504938 Solving -1 + x = -10.099504938 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 = -10.099504938 + 1 Combine like terms: -1 + 1 = 0 0 + x = -10.099504938 + 1 x = -10.099504938 + 1 Combine like terms: -10.099504938 + 1 = -9.099504938 x = -9.099504938 Simplifying x = -9.099504938Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.099504938, -9.099504938}
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