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Simplifying x2 + 12x + 30 = 5 Reorder the terms: 30 + 12x + x2 = 5 Solving 30 + 12x + x2 = 5 Solving for variable 'x'. Reorder the terms: 30 + -5 + 12x + x2 = 5 + -5 Combine like terms: 30 + -5 = 25 25 + 12x + x2 = 5 + -5 Combine like terms: 5 + -5 = 0 25 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + 12x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + 12x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 12x + x2 = 0 + -25 12x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 12x + x2 = -25 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 = -25 + 36 Reorder the terms: 36 + 12x + x2 = -25 + 36 Combine like terms: -25 + 36 = 11 36 + 12x + x2 = 11 Factor a perfect square on the left side: (x + 6)(x + 6) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + 6) equal to 3.31662479 and -3.31662479.Subproblem 1
x + 6 = 3.31662479 Simplifying x + 6 = 3.31662479 Reorder the terms: 6 + x = 3.31662479 Solving 6 + x = 3.31662479 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 = 3.31662479 + -6 Combine like terms: 6 + -6 = 0 0 + x = 3.31662479 + -6 x = 3.31662479 + -6 Combine like terms: 3.31662479 + -6 = -2.68337521 x = -2.68337521 Simplifying x = -2.68337521Subproblem 2
x + 6 = -3.31662479 Simplifying x + 6 = -3.31662479 Reorder the terms: 6 + x = -3.31662479 Solving 6 + x = -3.31662479 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 = -3.31662479 + -6 Combine like terms: 6 + -6 = 0 0 + x = -3.31662479 + -6 x = -3.31662479 + -6 Combine like terms: -3.31662479 + -6 = -9.31662479 x = -9.31662479 Simplifying x = -9.31662479Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.68337521, -9.31662479}
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