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Simplifying 8x2 + 16x = 25 Reorder the terms: 16x + 8x2 = 25 Solving 16x + 8x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + 16x + 8x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 16x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3.125 + 2x + x2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + 2x + 3.125 + x2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + 2x + x2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + 2x + x2 = 0 + 3.125 2x + x2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 2x + x2 = 3.125 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 = 3.125 + 1 Reorder the terms: 1 + 2x + x2 = 3.125 + 1 Combine like terms: 3.125 + 1 = 4.125 1 + 2x + x2 = 4.125 Factor a perfect square on the left side: (x + 1)(x + 1) = 4.125 Calculate the square root of the right side: 2.031009601 Break this problem into two subproblems by setting (x + 1) equal to 2.031009601 and -2.031009601.Subproblem 1
x + 1 = 2.031009601 Simplifying x + 1 = 2.031009601 Reorder the terms: 1 + x = 2.031009601 Solving 1 + x = 2.031009601 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 = 2.031009601 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.031009601 + -1 x = 2.031009601 + -1 Combine like terms: 2.031009601 + -1 = 1.031009601 x = 1.031009601 Simplifying x = 1.031009601Subproblem 2
x + 1 = -2.031009601 Simplifying x + 1 = -2.031009601 Reorder the terms: 1 + x = -2.031009601 Solving 1 + x = -2.031009601 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 = -2.031009601 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.031009601 + -1 x = -2.031009601 + -1 Combine like terms: -2.031009601 + -1 = -3.031009601 x = -3.031009601 Simplifying x = -3.031009601Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.031009601, -3.031009601}
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