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Simplifying x2 + -8x + -97 = 0 Reorder the terms: -97 + -8x + x2 = 0 Solving -97 + -8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '97' to each side of the equation. -97 + -8x + 97 + x2 = 0 + 97 Reorder the terms: -97 + 97 + -8x + x2 = 0 + 97 Combine like terms: -97 + 97 = 0 0 + -8x + x2 = 0 + 97 -8x + x2 = 0 + 97 Combine like terms: 0 + 97 = 97 -8x + x2 = 97 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 = 97 + 16 Reorder the terms: 16 + -8x + x2 = 97 + 16 Combine like terms: 97 + 16 = 113 16 + -8x + x2 = 113 Factor a perfect square on the left side: (x + -4)(x + -4) = 113 Calculate the square root of the right side: 10.630145813 Break this problem into two subproblems by setting (x + -4) equal to 10.630145813 and -10.630145813.Subproblem 1
x + -4 = 10.630145813 Simplifying x + -4 = 10.630145813 Reorder the terms: -4 + x = 10.630145813 Solving -4 + x = 10.630145813 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 = 10.630145813 + 4 Combine like terms: -4 + 4 = 0 0 + x = 10.630145813 + 4 x = 10.630145813 + 4 Combine like terms: 10.630145813 + 4 = 14.630145813 x = 14.630145813 Simplifying x = 14.630145813Subproblem 2
x + -4 = -10.630145813 Simplifying x + -4 = -10.630145813 Reorder the terms: -4 + x = -10.630145813 Solving -4 + x = -10.630145813 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 = -10.630145813 + 4 Combine like terms: -4 + 4 = 0 0 + x = -10.630145813 + 4 x = -10.630145813 + 4 Combine like terms: -10.630145813 + 4 = -6.630145813 x = -6.630145813 Simplifying x = -6.630145813Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.630145813, -6.630145813}
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