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Simplifying 16x2 + 25x = 4 Reorder the terms: 25x + 16x2 = 4 Solving 25x + 16x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + 25x + 16x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 25x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.25 + 1.5625x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 1.5625x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 1.5625x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 1.5625x + x2 = 0 + 0.25 1.5625x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 1.5625x + x2 = 0.25 The x term is 1.5625x. Take half its coefficient (0.78125). Square it (0.6103515625) and add it to both sides. Add '0.6103515625' to each side of the equation. 1.5625x + 0.6103515625 + x2 = 0.25 + 0.6103515625 Reorder the terms: 0.6103515625 + 1.5625x + x2 = 0.25 + 0.6103515625 Combine like terms: 0.25 + 0.6103515625 = 0.8603515625 0.6103515625 + 1.5625x + x2 = 0.8603515625 Factor a perfect square on the left side: (x + 0.78125)(x + 0.78125) = 0.8603515625 Calculate the square root of the right side: 0.92755138 Break this problem into two subproblems by setting (x + 0.78125) equal to 0.92755138 and -0.92755138.Subproblem 1
x + 0.78125 = 0.92755138 Simplifying x + 0.78125 = 0.92755138 Reorder the terms: 0.78125 + x = 0.92755138 Solving 0.78125 + x = 0.92755138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.78125' to each side of the equation. 0.78125 + -0.78125 + x = 0.92755138 + -0.78125 Combine like terms: 0.78125 + -0.78125 = 0.00000 0.00000 + x = 0.92755138 + -0.78125 x = 0.92755138 + -0.78125 Combine like terms: 0.92755138 + -0.78125 = 0.14630138 x = 0.14630138 Simplifying x = 0.14630138Subproblem 2
x + 0.78125 = -0.92755138 Simplifying x + 0.78125 = -0.92755138 Reorder the terms: 0.78125 + x = -0.92755138 Solving 0.78125 + x = -0.92755138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.78125' to each side of the equation. 0.78125 + -0.78125 + x = -0.92755138 + -0.78125 Combine like terms: 0.78125 + -0.78125 = 0.00000 0.00000 + x = -0.92755138 + -0.78125 x = -0.92755138 + -0.78125 Combine like terms: -0.92755138 + -0.78125 = -1.70880138 x = -1.70880138 Simplifying x = -1.70880138Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.14630138, -1.70880138}
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