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Simplifying x2 + 24x + 32 = 0 Reorder the terms: 32 + 24x + x2 = 0 Solving 32 + 24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + 24x + -32 + x2 = 0 + -32 Reorder the terms: 32 + -32 + 24x + x2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + 24x + x2 = 0 + -32 24x + x2 = 0 + -32 Combine like terms: 0 + -32 = -32 24x + x2 = -32 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 = -32 + 144 Reorder the terms: 144 + 24x + x2 = -32 + 144 Combine like terms: -32 + 144 = 112 144 + 24x + x2 = 112 Factor a perfect square on the left side: (x + 12)(x + 12) = 112 Calculate the square root of the right side: 10.583005244 Break this problem into two subproblems by setting (x + 12) equal to 10.583005244 and -10.583005244.Subproblem 1
x + 12 = 10.583005244 Simplifying x + 12 = 10.583005244 Reorder the terms: 12 + x = 10.583005244 Solving 12 + x = 10.583005244 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 = 10.583005244 + -12 Combine like terms: 12 + -12 = 0 0 + x = 10.583005244 + -12 x = 10.583005244 + -12 Combine like terms: 10.583005244 + -12 = -1.416994756 x = -1.416994756 Simplifying x = -1.416994756Subproblem 2
x + 12 = -10.583005244 Simplifying x + 12 = -10.583005244 Reorder the terms: 12 + x = -10.583005244 Solving 12 + x = -10.583005244 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 = -10.583005244 + -12 Combine like terms: 12 + -12 = 0 0 + x = -10.583005244 + -12 x = -10.583005244 + -12 Combine like terms: -10.583005244 + -12 = -22.583005244 x = -22.583005244 Simplifying x = -22.583005244Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.416994756, -22.583005244}
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