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Simplifying 8x * 8x + 3x = 5 Reorder the terms for easier multiplication: 8 * 8x * x + 3x = 5 Multiply 8 * 8 64x * x + 3x = 5 Multiply x * x 64x2 + 3x = 5 Reorder the terms: 3x + 64x2 = 5 Solving 3x + 64x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 3x + 64x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 3x + 64x2 = 0 Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. -0.078125 + 0.046875x + x2 = 0 Move the constant term to the right: Add '0.078125' to each side of the equation. -0.078125 + 0.046875x + 0.078125 + x2 = 0 + 0.078125 Reorder the terms: -0.078125 + 0.078125 + 0.046875x + x2 = 0 + 0.078125 Combine like terms: -0.078125 + 0.078125 = 0.000000 0.000000 + 0.046875x + x2 = 0 + 0.078125 0.046875x + x2 = 0 + 0.078125 Combine like terms: 0 + 0.078125 = 0.078125 0.046875x + x2 = 0.078125 The x term is 0.046875x. Take half its coefficient (0.0234375). Square it (0.0005493164063) and add it to both sides. Add '0.0005493164063' to each side of the equation. 0.046875x + 0.0005493164063 + x2 = 0.078125 + 0.0005493164063 Reorder the terms: 0.0005493164063 + 0.046875x + x2 = 0.078125 + 0.0005493164063 Combine like terms: 0.078125 + 0.0005493164063 = 0.0786743164063 0.0005493164063 + 0.046875x + x2 = 0.0786743164063 Factor a perfect square on the left side: (x + 0.0234375)(x + 0.0234375) = 0.0786743164063 Calculate the square root of the right side: 0.280489423 Break this problem into two subproblems by setting (x + 0.0234375) equal to 0.280489423 and -0.280489423.Subproblem 1
x + 0.0234375 = 0.280489423 Simplifying x + 0.0234375 = 0.280489423 Reorder the terms: 0.0234375 + x = 0.280489423 Solving 0.0234375 + x = 0.280489423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0234375' to each side of the equation. 0.0234375 + -0.0234375 + x = 0.280489423 + -0.0234375 Combine like terms: 0.0234375 + -0.0234375 = 0.0000000 0.0000000 + x = 0.280489423 + -0.0234375 x = 0.280489423 + -0.0234375 Combine like terms: 0.280489423 + -0.0234375 = 0.257051923 x = 0.257051923 Simplifying x = 0.257051923Subproblem 2
x + 0.0234375 = -0.280489423 Simplifying x + 0.0234375 = -0.280489423 Reorder the terms: 0.0234375 + x = -0.280489423 Solving 0.0234375 + x = -0.280489423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0234375' to each side of the equation. 0.0234375 + -0.0234375 + x = -0.280489423 + -0.0234375 Combine like terms: 0.0234375 + -0.0234375 = 0.0000000 0.0000000 + x = -0.280489423 + -0.0234375 x = -0.280489423 + -0.0234375 Combine like terms: -0.280489423 + -0.0234375 = -0.303926923 x = -0.303926923 Simplifying x = -0.303926923Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.257051923, -0.303926923}
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