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Simplifying x2 + 8x + -66 = 10 Reorder the terms: -66 + 8x + x2 = 10 Solving -66 + 8x + x2 = 10 Solving for variable 'x'. Reorder the terms: -66 + -10 + 8x + x2 = 10 + -10 Combine like terms: -66 + -10 = -76 -76 + 8x + x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -76 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '76' to each side of the equation. -76 + 8x + 76 + x2 = 0 + 76 Reorder the terms: -76 + 76 + 8x + x2 = 0 + 76 Combine like terms: -76 + 76 = 0 0 + 8x + x2 = 0 + 76 8x + x2 = 0 + 76 Combine like terms: 0 + 76 = 76 8x + x2 = 76 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 = 76 + 16 Reorder the terms: 16 + 8x + x2 = 76 + 16 Combine like terms: 76 + 16 = 92 16 + 8x + x2 = 92 Factor a perfect square on the left side: (x + 4)(x + 4) = 92 Calculate the square root of the right side: 9.591663047 Break this problem into two subproblems by setting (x + 4) equal to 9.591663047 and -9.591663047.Subproblem 1
x + 4 = 9.591663047 Simplifying x + 4 = 9.591663047 Reorder the terms: 4 + x = 9.591663047 Solving 4 + x = 9.591663047 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 = 9.591663047 + -4 Combine like terms: 4 + -4 = 0 0 + x = 9.591663047 + -4 x = 9.591663047 + -4 Combine like terms: 9.591663047 + -4 = 5.591663047 x = 5.591663047 Simplifying x = 5.591663047Subproblem 2
x + 4 = -9.591663047 Simplifying x + 4 = -9.591663047 Reorder the terms: 4 + x = -9.591663047 Solving 4 + x = -9.591663047 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 = -9.591663047 + -4 Combine like terms: 4 + -4 = 0 0 + x = -9.591663047 + -4 x = -9.591663047 + -4 Combine like terms: -9.591663047 + -4 = -13.591663047 x = -13.591663047 Simplifying x = -13.591663047Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.591663047, -13.591663047}
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