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Simplifying x2 + 15x + 54 = 12 Reorder the terms: 54 + 15x + x2 = 12 Solving 54 + 15x + x2 = 12 Solving for variable 'x'. Reorder the terms: 54 + -12 + 15x + x2 = 12 + -12 Combine like terms: 54 + -12 = 42 42 + 15x + x2 = 12 + -12 Combine like terms: 12 + -12 = 0 42 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-42' to each side of the equation. 42 + 15x + -42 + x2 = 0 + -42 Reorder the terms: 42 + -42 + 15x + x2 = 0 + -42 Combine like terms: 42 + -42 = 0 0 + 15x + x2 = 0 + -42 15x + x2 = 0 + -42 Combine like terms: 0 + -42 = -42 15x + x2 = -42 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = -42 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -42 + 56.25 Combine like terms: -42 + 56.25 = 14.25 56.25 + 15x + x2 = 14.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (x + 7.5) equal to 3.774917218 and -3.774917218.Subproblem 1
x + 7.5 = 3.774917218 Simplifying x + 7.5 = 3.774917218 Reorder the terms: 7.5 + x = 3.774917218 Solving 7.5 + x = 3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 3.774917218 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 3.774917218 + -7.5 x = 3.774917218 + -7.5 Combine like terms: 3.774917218 + -7.5 = -3.725082782 x = -3.725082782 Simplifying x = -3.725082782Subproblem 2
x + 7.5 = -3.774917218 Simplifying x + 7.5 = -3.774917218 Reorder the terms: 7.5 + x = -3.774917218 Solving 7.5 + x = -3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -3.774917218 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -3.774917218 + -7.5 x = -3.774917218 + -7.5 Combine like terms: -3.774917218 + -7.5 = -11.274917218 x = -11.274917218 Simplifying x = -11.274917218Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.725082782, -11.274917218}
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