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Simplifying x2 + 24x + 14 = 0 Reorder the terms: 14 + 24x + x2 = 0 Solving 14 + 24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 24x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + 24x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 24x + x2 = 0 + -14 24x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 24x + x2 = -14 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 = -14 + 144 Reorder the terms: 144 + 24x + x2 = -14 + 144 Combine like terms: -14 + 144 = 130 144 + 24x + x2 = 130 Factor a perfect square on the left side: (x + 12)(x + 12) = 130 Calculate the square root of the right side: 11.401754251 Break this problem into two subproblems by setting (x + 12) equal to 11.401754251 and -11.401754251.Subproblem 1
x + 12 = 11.401754251 Simplifying x + 12 = 11.401754251 Reorder the terms: 12 + x = 11.401754251 Solving 12 + x = 11.401754251 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 = 11.401754251 + -12 Combine like terms: 12 + -12 = 0 0 + x = 11.401754251 + -12 x = 11.401754251 + -12 Combine like terms: 11.401754251 + -12 = -0.598245749 x = -0.598245749 Simplifying x = -0.598245749Subproblem 2
x + 12 = -11.401754251 Simplifying x + 12 = -11.401754251 Reorder the terms: 12 + x = -11.401754251 Solving 12 + x = -11.401754251 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 = -11.401754251 + -12 Combine like terms: 12 + -12 = 0 0 + x = -11.401754251 + -12 x = -11.401754251 + -12 Combine like terms: -11.401754251 + -12 = -23.401754251 x = -23.401754251 Simplifying x = -23.401754251Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.598245749, -23.401754251}
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