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Simplifying x2 + 12x + 36 = 12.25 Reorder the terms: 36 + 12x + x2 = 12.25 Solving 36 + 12x + x2 = 12.25 Solving for variable 'x'. Reorder the terms: 36 + -12.25 + 12x + x2 = 12.25 + -12.25 Combine like terms: 36 + -12.25 = 23.75 23.75 + 12x + x2 = 12.25 + -12.25 Combine like terms: 12.25 + -12.25 = 0.00 23.75 + 12x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '-23.75' to each side of the equation. 23.75 + 12x + -23.75 + x2 = 0.00 + -23.75 Reorder the terms: 23.75 + -23.75 + 12x + x2 = 0.00 + -23.75 Combine like terms: 23.75 + -23.75 = 0.00 0.00 + 12x + x2 = 0.00 + -23.75 12x + x2 = 0.00 + -23.75 Combine like terms: 0.00 + -23.75 = -23.75 12x + x2 = -23.75 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 = -23.75 + 36 Reorder the terms: 36 + 12x + x2 = -23.75 + 36 Combine like terms: -23.75 + 36 = 12.25 36 + 12x + x2 = 12.25 Factor a perfect square on the left side: (x + 6)(x + 6) = 12.25 Calculate the square root of the right side: 3.5 Break this problem into two subproblems by setting (x + 6) equal to 3.5 and -3.5.Subproblem 1
x + 6 = 3.5 Simplifying x + 6 = 3.5 Reorder the terms: 6 + x = 3.5 Solving 6 + x = 3.5 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 = 3.5 + -6 Combine like terms: 6 + -6 = 0 0 + x = 3.5 + -6 x = 3.5 + -6 Combine like terms: 3.5 + -6 = -2.5 x = -2.5 Simplifying x = -2.5Subproblem 2
x + 6 = -3.5 Simplifying x + 6 = -3.5 Reorder the terms: 6 + x = -3.5 Solving 6 + x = -3.5 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 = -3.5 + -6 Combine like terms: 6 + -6 = 0 0 + x = -3.5 + -6 x = -3.5 + -6 Combine like terms: -3.5 + -6 = -9.5 x = -9.5 Simplifying x = -9.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.5, -9.5}
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