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Simplifying x2 + -12x + -22 = 64 Reorder the terms: -22 + -12x + x2 = 64 Solving -22 + -12x + x2 = 64 Solving for variable 'x'. Reorder the terms: -22 + -64 + -12x + x2 = 64 + -64 Combine like terms: -22 + -64 = -86 -86 + -12x + x2 = 64 + -64 Combine like terms: 64 + -64 = 0 -86 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '86' to each side of the equation. -86 + -12x + 86 + x2 = 0 + 86 Reorder the terms: -86 + 86 + -12x + x2 = 0 + 86 Combine like terms: -86 + 86 = 0 0 + -12x + x2 = 0 + 86 -12x + x2 = 0 + 86 Combine like terms: 0 + 86 = 86 -12x + x2 = 86 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 = 86 + 36 Reorder the terms: 36 + -12x + x2 = 86 + 36 Combine like terms: 86 + 36 = 122 36 + -12x + x2 = 122 Factor a perfect square on the left side: (x + -6)(x + -6) = 122 Calculate the square root of the right side: 11.045361017 Break this problem into two subproblems by setting (x + -6) equal to 11.045361017 and -11.045361017.Subproblem 1
x + -6 = 11.045361017 Simplifying x + -6 = 11.045361017 Reorder the terms: -6 + x = 11.045361017 Solving -6 + x = 11.045361017 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 = 11.045361017 + 6 Combine like terms: -6 + 6 = 0 0 + x = 11.045361017 + 6 x = 11.045361017 + 6 Combine like terms: 11.045361017 + 6 = 17.045361017 x = 17.045361017 Simplifying x = 17.045361017Subproblem 2
x + -6 = -11.045361017 Simplifying x + -6 = -11.045361017 Reorder the terms: -6 + x = -11.045361017 Solving -6 + x = -11.045361017 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 = -11.045361017 + 6 Combine like terms: -6 + 6 = 0 0 + x = -11.045361017 + 6 x = -11.045361017 + 6 Combine like terms: -11.045361017 + 6 = -5.045361017 x = -5.045361017 Simplifying x = -5.045361017Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.045361017, -5.045361017}
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