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Simplifying 4x2 + 31x + -4 = 0 Reorder the terms: -4 + 31x + 4x2 = 0 Solving -4 + 31x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1 + 7.75x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 7.75x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 7.75x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 7.75x + x2 = 0 + 1 7.75x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 7.75x + x2 = 1 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 = 1 + 15.015625 Reorder the terms: 15.015625 + 7.75x + x2 = 1 + 15.015625 Combine like terms: 1 + 15.015625 = 16.015625 15.015625 + 7.75x + x2 = 16.015625 Factor a perfect square on the left side: (x + 3.875)(x + 3.875) = 16.015625 Calculate the square root of the right side: 4.001952648 Break this problem into two subproblems by setting (x + 3.875) equal to 4.001952648 and -4.001952648.Subproblem 1
x + 3.875 = 4.001952648 Simplifying x + 3.875 = 4.001952648 Reorder the terms: 3.875 + x = 4.001952648 Solving 3.875 + x = 4.001952648 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 = 4.001952648 + -3.875 Combine like terms: 3.875 + -3.875 = 0.000 0.000 + x = 4.001952648 + -3.875 x = 4.001952648 + -3.875 Combine like terms: 4.001952648 + -3.875 = 0.126952648 x = 0.126952648 Simplifying x = 0.126952648Subproblem 2
x + 3.875 = -4.001952648 Simplifying x + 3.875 = -4.001952648 Reorder the terms: 3.875 + x = -4.001952648 Solving 3.875 + x = -4.001952648 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 = -4.001952648 + -3.875 Combine like terms: 3.875 + -3.875 = 0.000 0.000 + x = -4.001952648 + -3.875 x = -4.001952648 + -3.875 Combine like terms: -4.001952648 + -3.875 = -7.876952648 x = -7.876952648 Simplifying x = -7.876952648Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.126952648, -7.876952648}
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