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Simplifying x2 + -24x + 144 = 18 Reorder the terms: 144 + -24x + x2 = 18 Solving 144 + -24x + x2 = 18 Solving for variable 'x'. Reorder the terms: 144 + -18 + -24x + x2 = 18 + -18 Combine like terms: 144 + -18 = 126 126 + -24x + x2 = 18 + -18 Combine like terms: 18 + -18 = 0 126 + -24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-126' to each side of the equation. 126 + -24x + -126 + x2 = 0 + -126 Reorder the terms: 126 + -126 + -24x + x2 = 0 + -126 Combine like terms: 126 + -126 = 0 0 + -24x + x2 = 0 + -126 -24x + x2 = 0 + -126 Combine like terms: 0 + -126 = -126 -24x + x2 = -126 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = -126 + 144 Reorder the terms: 144 + -24x + x2 = -126 + 144 Combine like terms: -126 + 144 = 18 144 + -24x + x2 = 18 Factor a perfect square on the left side: (x + -12)(x + -12) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (x + -12) equal to 4.242640687 and -4.242640687.Subproblem 1
x + -12 = 4.242640687 Simplifying x + -12 = 4.242640687 Reorder the terms: -12 + x = 4.242640687 Solving -12 + x = 4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 4.242640687 + 12 Combine like terms: -12 + 12 = 0 0 + x = 4.242640687 + 12 x = 4.242640687 + 12 Combine like terms: 4.242640687 + 12 = 16.242640687 x = 16.242640687 Simplifying x = 16.242640687Subproblem 2
x + -12 = -4.242640687 Simplifying x + -12 = -4.242640687 Reorder the terms: -12 + x = -4.242640687 Solving -12 + x = -4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -4.242640687 + 12 Combine like terms: -12 + 12 = 0 0 + x = -4.242640687 + 12 x = -4.242640687 + 12 Combine like terms: -4.242640687 + 12 = 7.757359313 x = 7.757359313 Simplifying x = 7.757359313Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.242640687, 7.757359313}
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