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Simplifying 12x + 6 + x2 + 47 = 180 Reorder the terms: 6 + 47 + 12x + x2 = 180 Combine like terms: 6 + 47 = 53 53 + 12x + x2 = 180 Solving 53 + 12x + x2 = 180 Solving for variable 'x'. Reorder the terms: 53 + -180 + 12x + x2 = 180 + -180 Combine like terms: 53 + -180 = -127 -127 + 12x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -127 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '127' to each side of the equation. -127 + 12x + 127 + x2 = 0 + 127 Reorder the terms: -127 + 127 + 12x + x2 = 0 + 127 Combine like terms: -127 + 127 = 0 0 + 12x + x2 = 0 + 127 12x + x2 = 0 + 127 Combine like terms: 0 + 127 = 127 12x + x2 = 127 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 127 + 36 Reorder the terms: 36 + 12x + x2 = 127 + 36 Combine like terms: 127 + 36 = 163 36 + 12x + x2 = 163 Factor a perfect square on the left side: (x + 6)(x + 6) = 163 Calculate the square root of the right side: 12.767145335 Break this problem into two subproblems by setting (x + 6) equal to 12.767145335 and -12.767145335.Subproblem 1
x + 6 = 12.767145335 Simplifying x + 6 = 12.767145335 Reorder the terms: 6 + x = 12.767145335 Solving 6 + x = 12.767145335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 12.767145335 + -6 Combine like terms: 6 + -6 = 0 0 + x = 12.767145335 + -6 x = 12.767145335 + -6 Combine like terms: 12.767145335 + -6 = 6.767145335 x = 6.767145335 Simplifying x = 6.767145335Subproblem 2
x + 6 = -12.767145335 Simplifying x + 6 = -12.767145335 Reorder the terms: 6 + x = -12.767145335 Solving 6 + x = -12.767145335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -12.767145335 + -6 Combine like terms: 6 + -6 = 0 0 + x = -12.767145335 + -6 x = -12.767145335 + -6 Combine like terms: -12.767145335 + -6 = -18.767145335 x = -18.767145335 Simplifying x = -18.767145335Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.767145335, -18.767145335}
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