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Simplifying x + 23x2 = 487 Solving x + 23x2 = 487 Solving for variable 'x'. Reorder the terms: -487 + x + 23x2 = 487 + -487 Combine like terms: 487 + -487 = 0 -487 + x + 23x2 = 0 Begin completing the square. Divide all terms by 23 the coefficient of the squared term: Divide each side by '23'. -21.17391304 + 0.04347826087x + x2 = 0 Move the constant term to the right: Add '21.17391304' to each side of the equation. -21.17391304 + 0.04347826087x + 21.17391304 + x2 = 0 + 21.17391304 Reorder the terms: -21.17391304 + 21.17391304 + 0.04347826087x + x2 = 0 + 21.17391304 Combine like terms: -21.17391304 + 21.17391304 = 0.00000000 0.00000000 + 0.04347826087x + x2 = 0 + 21.17391304 0.04347826087x + x2 = 0 + 21.17391304 Combine like terms: 0 + 21.17391304 = 21.17391304 0.04347826087x + x2 = 21.17391304 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.04347826087x + 0.25 + x2 = 21.17391304 + 0.25 Reorder the terms: 0.25 + 0.04347826087x + x2 = 21.17391304 + 0.25 Combine like terms: 21.17391304 + 0.25 = 21.42391304 0.25 + 0.04347826087x + x2 = 21.42391304 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 21.42391304 Calculate the square root of the right side: 4.628597308 Break this problem into two subproblems by setting (x + 0.5) equal to 4.628597308 and -4.628597308.Subproblem 1
x + 0.5 = 4.628597308 Simplifying x + 0.5 = 4.628597308 Reorder the terms: 0.5 + x = 4.628597308 Solving 0.5 + x = 4.628597308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 4.628597308 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.628597308 + -0.5 x = 4.628597308 + -0.5 Combine like terms: 4.628597308 + -0.5 = 4.128597308 x = 4.128597308 Simplifying x = 4.128597308Subproblem 2
x + 0.5 = -4.628597308 Simplifying x + 0.5 = -4.628597308 Reorder the terms: 0.5 + x = -4.628597308 Solving 0.5 + x = -4.628597308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -4.628597308 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.628597308 + -0.5 x = -4.628597308 + -0.5 Combine like terms: -4.628597308 + -0.5 = -5.128597308 x = -5.128597308 Simplifying x = -5.128597308Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.128597308, -5.128597308}
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