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Simplifying x2 + 9 + 8x + 1 = 322 Reorder the terms: 9 + 1 + 8x + x2 = 322 Combine like terms: 9 + 1 = 10 10 + 8x + x2 = 322 Solving 10 + 8x + x2 = 322 Solving for variable 'x'. Reorder the terms: 10 + -322 + 8x + x2 = 322 + -322 Combine like terms: 10 + -322 = -312 -312 + 8x + x2 = 322 + -322 Combine like terms: 322 + -322 = 0 -312 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '312' to each side of the equation. -312 + 8x + 312 + x2 = 0 + 312 Reorder the terms: -312 + 312 + 8x + x2 = 0 + 312 Combine like terms: -312 + 312 = 0 0 + 8x + x2 = 0 + 312 8x + x2 = 0 + 312 Combine like terms: 0 + 312 = 312 8x + x2 = 312 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 312 + 16 Reorder the terms: 16 + 8x + x2 = 312 + 16 Combine like terms: 312 + 16 = 328 16 + 8x + x2 = 328 Factor a perfect square on the left side: (x + 4)(x + 4) = 328 Calculate the square root of the right side: 18.110770276 Break this problem into two subproblems by setting (x + 4) equal to 18.110770276 and -18.110770276.Subproblem 1
x + 4 = 18.110770276 Simplifying x + 4 = 18.110770276 Reorder the terms: 4 + x = 18.110770276 Solving 4 + x = 18.110770276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 18.110770276 + -4 Combine like terms: 4 + -4 = 0 0 + x = 18.110770276 + -4 x = 18.110770276 + -4 Combine like terms: 18.110770276 + -4 = 14.110770276 x = 14.110770276 Simplifying x = 14.110770276Subproblem 2
x + 4 = -18.110770276 Simplifying x + 4 = -18.110770276 Reorder the terms: 4 + x = -18.110770276 Solving 4 + x = -18.110770276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -18.110770276 + -4 Combine like terms: 4 + -4 = 0 0 + x = -18.110770276 + -4 x = -18.110770276 + -4 Combine like terms: -18.110770276 + -4 = -22.110770276 x = -22.110770276 Simplifying x = -22.110770276Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.110770276, -22.110770276}
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