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Simplifying x2 + 24x + 45 = 0 Reorder the terms: 45 + 24x + x2 = 0 Solving 45 + 24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-45' to each side of the equation. 45 + 24x + -45 + x2 = 0 + -45 Reorder the terms: 45 + -45 + 24x + x2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + 24x + x2 = 0 + -45 24x + x2 = 0 + -45 Combine like terms: 0 + -45 = -45 24x + x2 = -45 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 = -45 + 144 Reorder the terms: 144 + 24x + x2 = -45 + 144 Combine like terms: -45 + 144 = 99 144 + 24x + x2 = 99 Factor a perfect square on the left side: (x + 12)(x + 12) = 99 Calculate the square root of the right side: 9.949874371 Break this problem into two subproblems by setting (x + 12) equal to 9.949874371 and -9.949874371.Subproblem 1
x + 12 = 9.949874371 Simplifying x + 12 = 9.949874371 Reorder the terms: 12 + x = 9.949874371 Solving 12 + x = 9.949874371 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 = 9.949874371 + -12 Combine like terms: 12 + -12 = 0 0 + x = 9.949874371 + -12 x = 9.949874371 + -12 Combine like terms: 9.949874371 + -12 = -2.050125629 x = -2.050125629 Simplifying x = -2.050125629Subproblem 2
x + 12 = -9.949874371 Simplifying x + 12 = -9.949874371 Reorder the terms: 12 + x = -9.949874371 Solving 12 + x = -9.949874371 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 = -9.949874371 + -12 Combine like terms: 12 + -12 = 0 0 + x = -9.949874371 + -12 x = -9.949874371 + -12 Combine like terms: -9.949874371 + -12 = -21.949874371 x = -21.949874371 Simplifying x = -21.949874371Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.050125629, -21.949874371}
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