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Simplifying 4x2 + 16x + 11 = 0 Reorder the terms: 11 + 16x + 4x2 = 0 Solving 11 + 16x + 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'. 2.75 + 4x + x2 = 0 Move the constant term to the right: Add '-2.75' to each side of the equation. 2.75 + 4x + -2.75 + x2 = 0 + -2.75 Reorder the terms: 2.75 + -2.75 + 4x + x2 = 0 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + 4x + x2 = 0 + -2.75 4x + x2 = 0 + -2.75 Combine like terms: 0 + -2.75 = -2.75 4x + x2 = -2.75 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -2.75 + 4 Reorder the terms: 4 + 4x + x2 = -2.75 + 4 Combine like terms: -2.75 + 4 = 1.25 4 + 4x + x2 = 1.25 Factor a perfect square on the left side: (x + 2)(x + 2) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + 2) equal to 1.118033989 and -1.118033989.Subproblem 1
x + 2 = 1.118033989 Simplifying x + 2 = 1.118033989 Reorder the terms: 2 + x = 1.118033989 Solving 2 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.118033989 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.118033989 + -2 x = 1.118033989 + -2 Combine like terms: 1.118033989 + -2 = -0.881966011 x = -0.881966011 Simplifying x = -0.881966011Subproblem 2
x + 2 = -1.118033989 Simplifying x + 2 = -1.118033989 Reorder the terms: 2 + x = -1.118033989 Solving 2 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.118033989 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.118033989 + -2 x = -1.118033989 + -2 Combine like terms: -1.118033989 + -2 = -3.118033989 x = -3.118033989 Simplifying x = -3.118033989Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.881966011, -3.118033989}
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