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Simplifying x2 + 24x + -392 = 0 Reorder the terms: -392 + 24x + x2 = 0 Solving -392 + 24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '392' to each side of the equation. -392 + 24x + 392 + x2 = 0 + 392 Reorder the terms: -392 + 392 + 24x + x2 = 0 + 392 Combine like terms: -392 + 392 = 0 0 + 24x + x2 = 0 + 392 24x + x2 = 0 + 392 Combine like terms: 0 + 392 = 392 24x + x2 = 392 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 = 392 + 144 Reorder the terms: 144 + 24x + x2 = 392 + 144 Combine like terms: 392 + 144 = 536 144 + 24x + x2 = 536 Factor a perfect square on the left side: (x + 12)(x + 12) = 536 Calculate the square root of the right side: 23.151673806 Break this problem into two subproblems by setting (x + 12) equal to 23.151673806 and -23.151673806.Subproblem 1
x + 12 = 23.151673806 Simplifying x + 12 = 23.151673806 Reorder the terms: 12 + x = 23.151673806 Solving 12 + x = 23.151673806 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 = 23.151673806 + -12 Combine like terms: 12 + -12 = 0 0 + x = 23.151673806 + -12 x = 23.151673806 + -12 Combine like terms: 23.151673806 + -12 = 11.151673806 x = 11.151673806 Simplifying x = 11.151673806Subproblem 2
x + 12 = -23.151673806 Simplifying x + 12 = -23.151673806 Reorder the terms: 12 + x = -23.151673806 Solving 12 + x = -23.151673806 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 = -23.151673806 + -12 Combine like terms: 12 + -12 = 0 0 + x = -23.151673806 + -12 x = -23.151673806 + -12 Combine like terms: -23.151673806 + -12 = -35.151673806 x = -35.151673806 Simplifying x = -35.151673806Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.151673806, -35.151673806}
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