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Simplifying x2 + 24x + 55 = 0 Reorder the terms: 55 + 24x + x2 = 0 Solving 55 + 24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-55' to each side of the equation. 55 + 24x + -55 + x2 = 0 + -55 Reorder the terms: 55 + -55 + 24x + x2 = 0 + -55 Combine like terms: 55 + -55 = 0 0 + 24x + x2 = 0 + -55 24x + x2 = 0 + -55 Combine like terms: 0 + -55 = -55 24x + x2 = -55 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 = -55 + 144 Reorder the terms: 144 + 24x + x2 = -55 + 144 Combine like terms: -55 + 144 = 89 144 + 24x + x2 = 89 Factor a perfect square on the left side: (x + 12)(x + 12) = 89 Calculate the square root of the right side: 9.433981132 Break this problem into two subproblems by setting (x + 12) equal to 9.433981132 and -9.433981132.Subproblem 1
x + 12 = 9.433981132 Simplifying x + 12 = 9.433981132 Reorder the terms: 12 + x = 9.433981132 Solving 12 + x = 9.433981132 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 = 9.433981132 + -12 Combine like terms: 12 + -12 = 0 0 + x = 9.433981132 + -12 x = 9.433981132 + -12 Combine like terms: 9.433981132 + -12 = -2.566018868 x = -2.566018868 Simplifying x = -2.566018868Subproblem 2
x + 12 = -9.433981132 Simplifying x + 12 = -9.433981132 Reorder the terms: 12 + x = -9.433981132 Solving 12 + x = -9.433981132 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 = -9.433981132 + -12 Combine like terms: 12 + -12 = 0 0 + x = -9.433981132 + -12 x = -9.433981132 + -12 Combine like terms: -9.433981132 + -12 = -21.433981132 x = -21.433981132 Simplifying x = -21.433981132Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.566018868, -21.433981132}
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