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Simplifying 12x + x2 = 225 Solving 12x + x2 = 225 Solving for variable 'x'. Reorder the terms: -225 + 12x + x2 = 225 + -225 Combine like terms: 225 + -225 = 0 -225 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '225' to each side of the equation. -225 + 12x + 225 + x2 = 0 + 225 Reorder the terms: -225 + 225 + 12x + x2 = 0 + 225 Combine like terms: -225 + 225 = 0 0 + 12x + x2 = 0 + 225 12x + x2 = 0 + 225 Combine like terms: 0 + 225 = 225 12x + x2 = 225 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 = 225 + 36 Reorder the terms: 36 + 12x + x2 = 225 + 36 Combine like terms: 225 + 36 = 261 36 + 12x + x2 = 261 Factor a perfect square on the left side: (x + 6)(x + 6) = 261 Calculate the square root of the right side: 16.155494421 Break this problem into two subproblems by setting (x + 6) equal to 16.155494421 and -16.155494421.Subproblem 1
x + 6 = 16.155494421 Simplifying x + 6 = 16.155494421 Reorder the terms: 6 + x = 16.155494421 Solving 6 + x = 16.155494421 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 = 16.155494421 + -6 Combine like terms: 6 + -6 = 0 0 + x = 16.155494421 + -6 x = 16.155494421 + -6 Combine like terms: 16.155494421 + -6 = 10.155494421 x = 10.155494421 Simplifying x = 10.155494421Subproblem 2
x + 6 = -16.155494421 Simplifying x + 6 = -16.155494421 Reorder the terms: 6 + x = -16.155494421 Solving 6 + x = -16.155494421 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 = -16.155494421 + -6 Combine like terms: 6 + -6 = 0 0 + x = -16.155494421 + -6 x = -16.155494421 + -6 Combine like terms: -16.155494421 + -6 = -22.155494421 x = -22.155494421 Simplifying x = -22.155494421Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.155494421, -22.155494421}
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