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Simplifying 12x + x2 = 110 Solving 12x + x2 = 110 Solving for variable 'x'. Reorder the terms: -110 + 12x + x2 = 110 + -110 Combine like terms: 110 + -110 = 0 -110 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '110' to each side of the equation. -110 + 12x + 110 + x2 = 0 + 110 Reorder the terms: -110 + 110 + 12x + x2 = 0 + 110 Combine like terms: -110 + 110 = 0 0 + 12x + x2 = 0 + 110 12x + x2 = 0 + 110 Combine like terms: 0 + 110 = 110 12x + x2 = 110 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 = 110 + 36 Reorder the terms: 36 + 12x + x2 = 110 + 36 Combine like terms: 110 + 36 = 146 36 + 12x + x2 = 146 Factor a perfect square on the left side: (x + 6)(x + 6) = 146 Calculate the square root of the right side: 12.083045974 Break this problem into two subproblems by setting (x + 6) equal to 12.083045974 and -12.083045974.Subproblem 1
x + 6 = 12.083045974 Simplifying x + 6 = 12.083045974 Reorder the terms: 6 + x = 12.083045974 Solving 6 + x = 12.083045974 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 = 12.083045974 + -6 Combine like terms: 6 + -6 = 0 0 + x = 12.083045974 + -6 x = 12.083045974 + -6 Combine like terms: 12.083045974 + -6 = 6.083045974 x = 6.083045974 Simplifying x = 6.083045974Subproblem 2
x + 6 = -12.083045974 Simplifying x + 6 = -12.083045974 Reorder the terms: 6 + x = -12.083045974 Solving 6 + x = -12.083045974 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 = -12.083045974 + -6 Combine like terms: 6 + -6 = 0 0 + x = -12.083045974 + -6 x = -12.083045974 + -6 Combine like terms: -12.083045974 + -6 = -18.083045974 x = -18.083045974 Simplifying x = -18.083045974Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.083045974, -18.083045974}
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