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Simplifying (x + -1)(x + -1) + -32 = 0 Reorder the terms: (-1 + x)(x + -1) + -32 = 0 Reorder the terms: (-1 + x)(-1 + x) + -32 = 0 Multiply (-1 + x) * (-1 + x) (-1(-1 + x) + x(-1 + x)) + -32 = 0 ((-1 * -1 + x * -1) + x(-1 + x)) + -32 = 0 ((1 + -1x) + x(-1 + x)) + -32 = 0 (1 + -1x + (-1 * x + x * x)) + -32 = 0 (1 + -1x + (-1x + x2)) + -32 = 0 Combine like terms: -1x + -1x = -2x (1 + -2x + x2) + -32 = 0 Reorder the terms: 1 + -32 + -2x + x2 = 0 Combine like terms: 1 + -32 = -31 -31 + -2x + x2 = 0 Solving -31 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + -2x + 31 + x2 = 0 + 31 Reorder the terms: -31 + 31 + -2x + x2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + -2x + x2 = 0 + 31 -2x + x2 = 0 + 31 Combine like terms: 0 + 31 = 31 -2x + x2 = 31 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 = 31 + 1 Reorder the terms: 1 + -2x + x2 = 31 + 1 Combine like terms: 31 + 1 = 32 1 + -2x + x2 = 32 Factor a perfect square on the left side: (x + -1)(x + -1) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (x + -1) equal to 5.656854249 and -5.656854249.Subproblem 1
x + -1 = 5.656854249 Simplifying x + -1 = 5.656854249 Reorder the terms: -1 + x = 5.656854249 Solving -1 + x = 5.656854249 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 = 5.656854249 + 1 Combine like terms: -1 + 1 = 0 0 + x = 5.656854249 + 1 x = 5.656854249 + 1 Combine like terms: 5.656854249 + 1 = 6.656854249 x = 6.656854249 Simplifying x = 6.656854249Subproblem 2
x + -1 = -5.656854249 Simplifying x + -1 = -5.656854249 Reorder the terms: -1 + x = -5.656854249 Solving -1 + x = -5.656854249 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 = -5.656854249 + 1 Combine like terms: -1 + 1 = 0 0 + x = -5.656854249 + 1 x = -5.656854249 + 1 Combine like terms: -5.656854249 + 1 = -4.656854249 x = -4.656854249 Simplifying x = -4.656854249Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.656854249, -4.656854249}
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