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Simplifying x2 = 8x + 76 Reorder the terms: x2 = 76 + 8x Solving x2 = 76 + 8x Solving for variable 'x'. Reorder the terms: -76 + -8x + x2 = 76 + 8x + -76 + -8x Reorder the terms: -76 + -8x + x2 = 76 + -76 + 8x + -8x Combine like terms: 76 + -76 = 0 -76 + -8x + x2 = 0 + 8x + -8x -76 + -8x + x2 = 8x + -8x Combine like terms: 8x + -8x = 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 = 13.591663047 x = 13.591663047 Simplifying x = 13.591663047Subproblem 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 = -5.591663047 x = -5.591663047 Simplifying x = -5.591663047Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.591663047, -5.591663047}
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