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Simplifying x2 + 8x + 11 = 66 Reorder the terms: 11 + 8x + x2 = 66 Solving 11 + 8x + x2 = 66 Solving for variable 'x'. Reorder the terms: 11 + -66 + 8x + x2 = 66 + -66 Combine like terms: 11 + -66 = -55 -55 + 8x + x2 = 66 + -66 Combine like terms: 66 + -66 = 0 -55 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '55' to each side of the equation. -55 + 8x + 55 + x2 = 0 + 55 Reorder the terms: -55 + 55 + 8x + x2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + 8x + x2 = 0 + 55 8x + x2 = 0 + 55 Combine like terms: 0 + 55 = 55 8x + x2 = 55 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 = 55 + 16 Reorder the terms: 16 + 8x + x2 = 55 + 16 Combine like terms: 55 + 16 = 71 16 + 8x + x2 = 71 Factor a perfect square on the left side: (x + 4)(x + 4) = 71 Calculate the square root of the right side: 8.426149773 Break this problem into two subproblems by setting (x + 4) equal to 8.426149773 and -8.426149773.Subproblem 1
x + 4 = 8.426149773 Simplifying x + 4 = 8.426149773 Reorder the terms: 4 + x = 8.426149773 Solving 4 + x = 8.426149773 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 = 8.426149773 + -4 Combine like terms: 4 + -4 = 0 0 + x = 8.426149773 + -4 x = 8.426149773 + -4 Combine like terms: 8.426149773 + -4 = 4.426149773 x = 4.426149773 Simplifying x = 4.426149773Subproblem 2
x + 4 = -8.426149773 Simplifying x + 4 = -8.426149773 Reorder the terms: 4 + x = -8.426149773 Solving 4 + x = -8.426149773 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 = -8.426149773 + -4 Combine like terms: 4 + -4 = 0 0 + x = -8.426149773 + -4 x = -8.426149773 + -4 Combine like terms: -8.426149773 + -4 = -12.426149773 x = -12.426149773 Simplifying x = -12.426149773Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.426149773, -12.426149773}
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