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Simplifying x2 + 24x + 54 = 0 Reorder the terms: 54 + 24x + x2 = 0 Solving 54 + 24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-54' to each side of the equation. 54 + 24x + -54 + x2 = 0 + -54 Reorder the terms: 54 + -54 + 24x + x2 = 0 + -54 Combine like terms: 54 + -54 = 0 0 + 24x + x2 = 0 + -54 24x + x2 = 0 + -54 Combine like terms: 0 + -54 = -54 24x + x2 = -54 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 = -54 + 144 Reorder the terms: 144 + 24x + x2 = -54 + 144 Combine like terms: -54 + 144 = 90 144 + 24x + x2 = 90 Factor a perfect square on the left side: (x + 12)(x + 12) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (x + 12) equal to 9.486832981 and -9.486832981.Subproblem 1
x + 12 = 9.486832981 Simplifying x + 12 = 9.486832981 Reorder the terms: 12 + x = 9.486832981 Solving 12 + x = 9.486832981 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 = 9.486832981 + -12 Combine like terms: 12 + -12 = 0 0 + x = 9.486832981 + -12 x = 9.486832981 + -12 Combine like terms: 9.486832981 + -12 = -2.513167019 x = -2.513167019 Simplifying x = -2.513167019Subproblem 2
x + 12 = -9.486832981 Simplifying x + 12 = -9.486832981 Reorder the terms: 12 + x = -9.486832981 Solving 12 + x = -9.486832981 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 = -9.486832981 + -12 Combine like terms: 12 + -12 = 0 0 + x = -9.486832981 + -12 x = -9.486832981 + -12 Combine like terms: -9.486832981 + -12 = -21.486832981 x = -21.486832981 Simplifying x = -21.486832981Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.513167019, -21.486832981}
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