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Simplifying 4x2 + 24x + 31 = 0 Reorder the terms: 31 + 24x + 4x2 = 0 Solving 31 + 24x + 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'. 7.75 + 6x + x2 = 0 Move the constant term to the right: Add '-7.75' to each side of the equation. 7.75 + 6x + -7.75 + x2 = 0 + -7.75 Reorder the terms: 7.75 + -7.75 + 6x + x2 = 0 + -7.75 Combine like terms: 7.75 + -7.75 = 0.00 0.00 + 6x + x2 = 0 + -7.75 6x + x2 = 0 + -7.75 Combine like terms: 0 + -7.75 = -7.75 6x + x2 = -7.75 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -7.75 + 9 Reorder the terms: 9 + 6x + x2 = -7.75 + 9 Combine like terms: -7.75 + 9 = 1.25 9 + 6x + x2 = 1.25 Factor a perfect square on the left side: (x + 3)(x + 3) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + 3) equal to 1.118033989 and -1.118033989.Subproblem 1
x + 3 = 1.118033989 Simplifying x + 3 = 1.118033989 Reorder the terms: 3 + x = 1.118033989 Solving 3 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 1.118033989 + -3 Combine like terms: 3 + -3 = 0 0 + x = 1.118033989 + -3 x = 1.118033989 + -3 Combine like terms: 1.118033989 + -3 = -1.881966011 x = -1.881966011 Simplifying x = -1.881966011Subproblem 2
x + 3 = -1.118033989 Simplifying x + 3 = -1.118033989 Reorder the terms: 3 + x = -1.118033989 Solving 3 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -1.118033989 + -3 Combine like terms: 3 + -3 = 0 0 + x = -1.118033989 + -3 x = -1.118033989 + -3 Combine like terms: -1.118033989 + -3 = -4.118033989 x = -4.118033989 Simplifying x = -4.118033989Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.881966011, -4.118033989}
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