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Simplifying x = 97 + -16x2 Solving x = 97 + -16x2 Solving for variable 'x'. Reorder the terms: -97 + x + 16x2 = 97 + -16x2 + -97 + 16x2 Reorder the terms: -97 + x + 16x2 = 97 + -97 + -16x2 + 16x2 Combine like terms: 97 + -97 = 0 -97 + x + 16x2 = 0 + -16x2 + 16x2 -97 + x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -97 + x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -6.0625 + 0.0625x + x2 = 0 Move the constant term to the right: Add '6.0625' to each side of the equation. -6.0625 + 0.0625x + 6.0625 + x2 = 0 + 6.0625 Reorder the terms: -6.0625 + 6.0625 + 0.0625x + x2 = 0 + 6.0625 Combine like terms: -6.0625 + 6.0625 = 0.0000 0.0000 + 0.0625x + x2 = 0 + 6.0625 0.0625x + x2 = 0 + 6.0625 Combine like terms: 0 + 6.0625 = 6.0625 0.0625x + x2 = 6.0625 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.0625x + 0.25 + x2 = 6.0625 + 0.25 Reorder the terms: 0.25 + 0.0625x + x2 = 6.0625 + 0.25 Combine like terms: 6.0625 + 0.25 = 6.3125 0.25 + 0.0625x + x2 = 6.3125 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 6.3125 Calculate the square root of the right side: 2.512468905 Break this problem into two subproblems by setting (x + 0.5) equal to 2.512468905 and -2.512468905.Subproblem 1
x + 0.5 = 2.512468905 Simplifying x + 0.5 = 2.512468905 Reorder the terms: 0.5 + x = 2.512468905 Solving 0.5 + x = 2.512468905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.512468905 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.512468905 + -0.5 x = 2.512468905 + -0.5 Combine like terms: 2.512468905 + -0.5 = 2.012468905 x = 2.012468905 Simplifying x = 2.012468905Subproblem 2
x + 0.5 = -2.512468905 Simplifying x + 0.5 = -2.512468905 Reorder the terms: 0.5 + x = -2.512468905 Solving 0.5 + x = -2.512468905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.512468905 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.512468905 + -0.5 x = -2.512468905 + -0.5 Combine like terms: -2.512468905 + -0.5 = -3.012468905 x = -3.012468905 Simplifying x = -3.012468905Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.012468905, -3.012468905}
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