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Simplifying 4x2 + 31x = 42 Reorder the terms: 31x + 4x2 = 42 Solving 31x + 4x2 = 42 Solving for variable 'x'. Reorder the terms: -42 + 31x + 4x2 = 42 + -42 Combine like terms: 42 + -42 = 0 -42 + 31x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -10.5 + 7.75x + x2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + 7.75x + 10.5 + x2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + 7.75x + x2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + 7.75x + x2 = 0 + 10.5 7.75x + x2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 7.75x + x2 = 10.5 The x term is 7.75x. Take half its coefficient (3.875). Square it (15.015625) and add it to both sides. Add '15.015625' to each side of the equation. 7.75x + 15.015625 + x2 = 10.5 + 15.015625 Reorder the terms: 15.015625 + 7.75x + x2 = 10.5 + 15.015625 Combine like terms: 10.5 + 15.015625 = 25.515625 15.015625 + 7.75x + x2 = 25.515625 Factor a perfect square on the left side: (x + 3.875)(x + 3.875) = 25.515625 Calculate the square root of the right side: 5.051299338 Break this problem into two subproblems by setting (x + 3.875) equal to 5.051299338 and -5.051299338.Subproblem 1
x + 3.875 = 5.051299338 Simplifying x + 3.875 = 5.051299338 Reorder the terms: 3.875 + x = 5.051299338 Solving 3.875 + x = 5.051299338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.875' to each side of the equation. 3.875 + -3.875 + x = 5.051299338 + -3.875 Combine like terms: 3.875 + -3.875 = 0.000 0.000 + x = 5.051299338 + -3.875 x = 5.051299338 + -3.875 Combine like terms: 5.051299338 + -3.875 = 1.176299338 x = 1.176299338 Simplifying x = 1.176299338Subproblem 2
x + 3.875 = -5.051299338 Simplifying x + 3.875 = -5.051299338 Reorder the terms: 3.875 + x = -5.051299338 Solving 3.875 + x = -5.051299338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.875' to each side of the equation. 3.875 + -3.875 + x = -5.051299338 + -3.875 Combine like terms: 3.875 + -3.875 = 0.000 0.000 + x = -5.051299338 + -3.875 x = -5.051299338 + -3.875 Combine like terms: -5.051299338 + -3.875 = -8.926299338 x = -8.926299338 Simplifying x = -8.926299338Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.176299338, -8.926299338}
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