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Simplifying 3x + 6x2 = 500 Solving 3x + 6x2 = 500 Solving for variable 'x'. Reorder the terms: -500 + 3x + 6x2 = 500 + -500 Combine like terms: 500 + -500 = 0 -500 + 3x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -83.33333333 + 0.5x + x2 = 0 Move the constant term to the right: Add '83.33333333' to each side of the equation. -83.33333333 + 0.5x + 83.33333333 + x2 = 0 + 83.33333333 Reorder the terms: -83.33333333 + 83.33333333 + 0.5x + x2 = 0 + 83.33333333 Combine like terms: -83.33333333 + 83.33333333 = 0.00000000 0.00000000 + 0.5x + x2 = 0 + 83.33333333 0.5x + x2 = 0 + 83.33333333 Combine like terms: 0 + 83.33333333 = 83.33333333 0.5x + x2 = 83.33333333 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 83.33333333 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 83.33333333 + 0.0625 Combine like terms: 83.33333333 + 0.0625 = 83.39583333 0.0625 + 0.5x + x2 = 83.39583333 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 83.39583333 Calculate the square root of the right side: 9.132131916 Break this problem into two subproblems by setting (x + 0.25) equal to 9.132131916 and -9.132131916.Subproblem 1
x + 0.25 = 9.132131916 Simplifying x + 0.25 = 9.132131916 Reorder the terms: 0.25 + x = 9.132131916 Solving 0.25 + x = 9.132131916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 9.132131916 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 9.132131916 + -0.25 x = 9.132131916 + -0.25 Combine like terms: 9.132131916 + -0.25 = 8.882131916 x = 8.882131916 Simplifying x = 8.882131916Subproblem 2
x + 0.25 = -9.132131916 Simplifying x + 0.25 = -9.132131916 Reorder the terms: 0.25 + x = -9.132131916 Solving 0.25 + x = -9.132131916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -9.132131916 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -9.132131916 + -0.25 x = -9.132131916 + -0.25 Combine like terms: -9.132131916 + -0.25 = -9.382131916 x = -9.382131916 Simplifying x = -9.382131916Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.882131916, -9.382131916}
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