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Simplifying x2 + 14x + 12 = 180 Reorder the terms: 12 + 14x + x2 = 180 Solving 12 + 14x + x2 = 180 Solving for variable 'x'. Reorder the terms: 12 + -180 + 14x + x2 = 180 + -180 Combine like terms: 12 + -180 = -168 -168 + 14x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -168 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '168' to each side of the equation. -168 + 14x + 168 + x2 = 0 + 168 Reorder the terms: -168 + 168 + 14x + x2 = 0 + 168 Combine like terms: -168 + 168 = 0 0 + 14x + x2 = 0 + 168 14x + x2 = 0 + 168 Combine like terms: 0 + 168 = 168 14x + x2 = 168 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 168 + 49 Reorder the terms: 49 + 14x + x2 = 168 + 49 Combine like terms: 168 + 49 = 217 49 + 14x + x2 = 217 Factor a perfect square on the left side: (x + 7)(x + 7) = 217 Calculate the square root of the right side: 14.730919863 Break this problem into two subproblems by setting (x + 7) equal to 14.730919863 and -14.730919863.Subproblem 1
x + 7 = 14.730919863 Simplifying x + 7 = 14.730919863 Reorder the terms: 7 + x = 14.730919863 Solving 7 + x = 14.730919863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 14.730919863 + -7 Combine like terms: 7 + -7 = 0 0 + x = 14.730919863 + -7 x = 14.730919863 + -7 Combine like terms: 14.730919863 + -7 = 7.730919863 x = 7.730919863 Simplifying x = 7.730919863Subproblem 2
x + 7 = -14.730919863 Simplifying x + 7 = -14.730919863 Reorder the terms: 7 + x = -14.730919863 Solving 7 + x = -14.730919863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -14.730919863 + -7 Combine like terms: 7 + -7 = 0 0 + x = -14.730919863 + -7 x = -14.730919863 + -7 Combine like terms: -14.730919863 + -7 = -21.730919863 x = -21.730919863 Simplifying x = -21.730919863Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.730919863, -21.730919863}
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