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Simplifying (6 + x + 4)(x + 6) = 300 Reorder the terms: (6 + 4 + x)(x + 6) = 300 Combine like terms: 6 + 4 = 10 (10 + x)(x + 6) = 300 Reorder the terms: (10 + x)(6 + x) = 300 Multiply (10 + x) * (6 + x) (10(6 + x) + x(6 + x)) = 300 ((6 * 10 + x * 10) + x(6 + x)) = 300 ((60 + 10x) + x(6 + x)) = 300 (60 + 10x + (6 * x + x * x)) = 300 (60 + 10x + (6x + x2)) = 300 Combine like terms: 10x + 6x = 16x (60 + 16x + x2) = 300 Solving 60 + 16x + x2 = 300 Solving for variable 'x'. Reorder the terms: 60 + -300 + 16x + x2 = 300 + -300 Combine like terms: 60 + -300 = -240 -240 + 16x + x2 = 300 + -300 Combine like terms: 300 + -300 = 0 -240 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '240' to each side of the equation. -240 + 16x + 240 + x2 = 0 + 240 Reorder the terms: -240 + 240 + 16x + x2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + 16x + x2 = 0 + 240 16x + x2 = 0 + 240 Combine like terms: 0 + 240 = 240 16x + x2 = 240 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 240 + 64 Reorder the terms: 64 + 16x + x2 = 240 + 64 Combine like terms: 240 + 64 = 304 64 + 16x + x2 = 304 Factor a perfect square on the left side: (x + 8)(x + 8) = 304 Calculate the square root of the right side: 17.435595774 Break this problem into two subproblems by setting (x + 8) equal to 17.435595774 and -17.435595774.Subproblem 1
x + 8 = 17.435595774 Simplifying x + 8 = 17.435595774 Reorder the terms: 8 + x = 17.435595774 Solving 8 + x = 17.435595774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 17.435595774 + -8 Combine like terms: 8 + -8 = 0 0 + x = 17.435595774 + -8 x = 17.435595774 + -8 Combine like terms: 17.435595774 + -8 = 9.435595774 x = 9.435595774 Simplifying x = 9.435595774Subproblem 2
x + 8 = -17.435595774 Simplifying x + 8 = -17.435595774 Reorder the terms: 8 + x = -17.435595774 Solving 8 + x = -17.435595774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -17.435595774 + -8 Combine like terms: 8 + -8 = 0 0 + x = -17.435595774 + -8 x = -17.435595774 + -8 Combine like terms: -17.435595774 + -8 = -25.435595774 x = -25.435595774 Simplifying x = -25.435595774Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.435595774, -25.435595774}
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