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Simplifying x2 + 6x + 6x + 20 = 8 Reorder the terms: 20 + 6x + 6x + x2 = 8 Combine like terms: 6x + 6x = 12x 20 + 12x + x2 = 8 Solving 20 + 12x + x2 = 8 Solving for variable 'x'. Reorder the terms: 20 + -8 + 12x + x2 = 8 + -8 Combine like terms: 20 + -8 = 12 12 + 12x + x2 = 8 + -8 Combine like terms: 8 + -8 = 0 12 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 12x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + 12x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 12x + x2 = 0 + -12 12x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 12x + x2 = -12 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 = -12 + 36 Reorder the terms: 36 + 12x + x2 = -12 + 36 Combine like terms: -12 + 36 = 24 36 + 12x + x2 = 24 Factor a perfect square on the left side: (x + 6)(x + 6) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (x + 6) equal to 4.898979486 and -4.898979486.Subproblem 1
x + 6 = 4.898979486 Simplifying x + 6 = 4.898979486 Reorder the terms: 6 + x = 4.898979486 Solving 6 + x = 4.898979486 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 = 4.898979486 + -6 Combine like terms: 6 + -6 = 0 0 + x = 4.898979486 + -6 x = 4.898979486 + -6 Combine like terms: 4.898979486 + -6 = -1.101020514 x = -1.101020514 Simplifying x = -1.101020514Subproblem 2
x + 6 = -4.898979486 Simplifying x + 6 = -4.898979486 Reorder the terms: 6 + x = -4.898979486 Solving 6 + x = -4.898979486 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 = -4.898979486 + -6 Combine like terms: 6 + -6 = 0 0 + x = -4.898979486 + -6 x = -4.898979486 + -6 Combine like terms: -4.898979486 + -6 = -10.898979486 x = -10.898979486 Simplifying x = -10.898979486Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.101020514, -10.898979486}
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