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Simplifying 8x2 + 16x = 41 Reorder the terms: 16x + 8x2 = 41 Solving 16x + 8x2 = 41 Solving for variable 'x'. Reorder the terms: -41 + 16x + 8x2 = 41 + -41 Combine like terms: 41 + -41 = 0 -41 + 16x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -5.125 + 2x + x2 = 0 Move the constant term to the right: Add '5.125' to each side of the equation. -5.125 + 2x + 5.125 + x2 = 0 + 5.125 Reorder the terms: -5.125 + 5.125 + 2x + x2 = 0 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + 2x + x2 = 0 + 5.125 2x + x2 = 0 + 5.125 Combine like terms: 0 + 5.125 = 5.125 2x + x2 = 5.125 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 5.125 + 1 Reorder the terms: 1 + 2x + x2 = 5.125 + 1 Combine like terms: 5.125 + 1 = 6.125 1 + 2x + x2 = 6.125 Factor a perfect square on the left side: (x + 1)(x + 1) = 6.125 Calculate the square root of the right side: 2.474873734 Break this problem into two subproblems by setting (x + 1) equal to 2.474873734 and -2.474873734.Subproblem 1
x + 1 = 2.474873734 Simplifying x + 1 = 2.474873734 Reorder the terms: 1 + x = 2.474873734 Solving 1 + x = 2.474873734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.474873734 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.474873734 + -1 x = 2.474873734 + -1 Combine like terms: 2.474873734 + -1 = 1.474873734 x = 1.474873734 Simplifying x = 1.474873734Subproblem 2
x + 1 = -2.474873734 Simplifying x + 1 = -2.474873734 Reorder the terms: 1 + x = -2.474873734 Solving 1 + x = -2.474873734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.474873734 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.474873734 + -1 x = -2.474873734 + -1 Combine like terms: -2.474873734 + -1 = -3.474873734 x = -3.474873734 Simplifying x = -3.474873734Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.474873734, -3.474873734}
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