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Simplifying 8x2 + 5x = 8 Reorder the terms: 5x + 8x2 = 8 Solving 5x + 8x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + 5x + 8x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 5x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1 + 0.625x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.625x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.625x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.625x + x2 = 0 + 1 0.625x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.625x + x2 = 1 The x term is 0.625x. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625x + 0.09765625 + x2 = 1 + 0.09765625 Reorder the terms: 0.09765625 + 0.625x + x2 = 1 + 0.09765625 Combine like terms: 1 + 0.09765625 = 1.09765625 0.09765625 + 0.625x + x2 = 1.09765625 Factor a perfect square on the left side: (x + 0.3125)(x + 0.3125) = 1.09765625 Calculate the square root of the right side: 1.047690913 Break this problem into two subproblems by setting (x + 0.3125) equal to 1.047690913 and -1.047690913.Subproblem 1
x + 0.3125 = 1.047690913 Simplifying x + 0.3125 = 1.047690913 Reorder the terms: 0.3125 + x = 1.047690913 Solving 0.3125 + x = 1.047690913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + x = 1.047690913 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x = 1.047690913 + -0.3125 x = 1.047690913 + -0.3125 Combine like terms: 1.047690913 + -0.3125 = 0.735190913 x = 0.735190913 Simplifying x = 0.735190913Subproblem 2
x + 0.3125 = -1.047690913 Simplifying x + 0.3125 = -1.047690913 Reorder the terms: 0.3125 + x = -1.047690913 Solving 0.3125 + x = -1.047690913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + x = -1.047690913 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x = -1.047690913 + -0.3125 x = -1.047690913 + -0.3125 Combine like terms: -1.047690913 + -0.3125 = -1.360190913 x = -1.360190913 Simplifying x = -1.360190913Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.735190913, -1.360190913}
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