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Simplifying x2 + -12x + 32 = 9 Reorder the terms: 32 + -12x + x2 = 9 Solving 32 + -12x + x2 = 9 Solving for variable 'x'. Reorder the terms: 32 + -9 + -12x + x2 = 9 + -9 Combine like terms: 32 + -9 = 23 23 + -12x + x2 = 9 + -9 Combine like terms: 9 + -9 = 0 23 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-23' to each side of the equation. 23 + -12x + -23 + x2 = 0 + -23 Reorder the terms: 23 + -23 + -12x + x2 = 0 + -23 Combine like terms: 23 + -23 = 0 0 + -12x + x2 = 0 + -23 -12x + x2 = 0 + -23 Combine like terms: 0 + -23 = -23 -12x + x2 = -23 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 = -23 + 36 Reorder the terms: 36 + -12x + x2 = -23 + 36 Combine like terms: -23 + 36 = 13 36 + -12x + x2 = 13 Factor a perfect square on the left side: (x + -6)(x + -6) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (x + -6) equal to 3.605551275 and -3.605551275.Subproblem 1
x + -6 = 3.605551275 Simplifying x + -6 = 3.605551275 Reorder the terms: -6 + x = 3.605551275 Solving -6 + x = 3.605551275 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 = 3.605551275 + 6 Combine like terms: -6 + 6 = 0 0 + x = 3.605551275 + 6 x = 3.605551275 + 6 Combine like terms: 3.605551275 + 6 = 9.605551275 x = 9.605551275 Simplifying x = 9.605551275Subproblem 2
x + -6 = -3.605551275 Simplifying x + -6 = -3.605551275 Reorder the terms: -6 + x = -3.605551275 Solving -6 + x = -3.605551275 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 = -3.605551275 + 6 Combine like terms: -6 + 6 = 0 0 + x = -3.605551275 + 6 x = -3.605551275 + 6 Combine like terms: -3.605551275 + 6 = 2.394448725 x = 2.394448725 Simplifying x = 2.394448725Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.605551275, 2.394448725}
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