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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 = -42 -42 + -12x + x2 = 64 + -64 Combine like terms: 64 + -64 = 0 -42 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + -12x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + -12x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -12x + x2 = 0 + 42 -12x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 -12x + x2 = 42 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 = 42 + 36 Reorder the terms: 36 + -12x + x2 = 42 + 36 Combine like terms: 42 + 36 = 78 36 + -12x + x2 = 78 Factor a perfect square on the left side: (x + -6)(x + -6) = 78 Calculate the square root of the right side: 8.831760866 Break this problem into two subproblems by setting (x + -6) equal to 8.831760866 and -8.831760866.Subproblem 1
x + -6 = 8.831760866 Simplifying x + -6 = 8.831760866 Reorder the terms: -6 + x = 8.831760866 Solving -6 + x = 8.831760866 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 = 8.831760866 + 6 Combine like terms: -6 + 6 = 0 0 + x = 8.831760866 + 6 x = 8.831760866 + 6 Combine like terms: 8.831760866 + 6 = 14.831760866 x = 14.831760866 Simplifying x = 14.831760866Subproblem 2
x + -6 = -8.831760866 Simplifying x + -6 = -8.831760866 Reorder the terms: -6 + x = -8.831760866 Solving -6 + x = -8.831760866 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 = -8.831760866 + 6 Combine like terms: -6 + 6 = 0 0 + x = -8.831760866 + 6 x = -8.831760866 + 6 Combine like terms: -8.831760866 + 6 = -2.831760866 x = -2.831760866 Simplifying x = -2.831760866Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.831760866, -2.831760866}
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