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Simplifying (x * x) + 12x = 24 Multiply x * x (x2) + 12x = 24 x2 + 12x = 24 Reorder the terms: 12x + x2 = 24 Solving 12x + x2 = 24 Solving for variable 'x'. Reorder the terms: -24 + 12x + x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + 12x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 12x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 12x + x2 = 0 + 24 12x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 12x + x2 = 24 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 = 24 + 36 Reorder the terms: 36 + 12x + x2 = 24 + 36 Combine like terms: 24 + 36 = 60 36 + 12x + x2 = 60 Factor a perfect square on the left side: (x + 6)(x + 6) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (x + 6) equal to 7.745966692 and -7.745966692.Subproblem 1
x + 6 = 7.745966692 Simplifying x + 6 = 7.745966692 Reorder the terms: 6 + x = 7.745966692 Solving 6 + x = 7.745966692 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 = 7.745966692 + -6 Combine like terms: 6 + -6 = 0 0 + x = 7.745966692 + -6 x = 7.745966692 + -6 Combine like terms: 7.745966692 + -6 = 1.745966692 x = 1.745966692 Simplifying x = 1.745966692Subproblem 2
x + 6 = -7.745966692 Simplifying x + 6 = -7.745966692 Reorder the terms: 6 + x = -7.745966692 Solving 6 + x = -7.745966692 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 = -7.745966692 + -6 Combine like terms: 6 + -6 = 0 0 + x = -7.745966692 + -6 x = -7.745966692 + -6 Combine like terms: -7.745966692 + -6 = -13.745966692 x = -13.745966692 Simplifying x = -13.745966692Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.745966692, -13.745966692}
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