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Simplifying (3x2) + 12x + 11 = 0 Reorder the terms: 11 + 12x + (3x2) = 0 Solving 11 + 12x + (3x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3.666666667 + 4x + x2 = 0 Move the constant term to the right: Add '-3.666666667' to each side of the equation. 3.666666667 + 4x + -3.666666667 + x2 = 0 + -3.666666667 Reorder the terms: 3.666666667 + -3.666666667 + 4x + x2 = 0 + -3.666666667 Combine like terms: 3.666666667 + -3.666666667 = 0.000000000 0.000000000 + 4x + x2 = 0 + -3.666666667 4x + x2 = 0 + -3.666666667 Combine like terms: 0 + -3.666666667 = -3.666666667 4x + x2 = -3.666666667 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 = -3.666666667 + 4 Reorder the terms: 4 + 4x + x2 = -3.666666667 + 4 Combine like terms: -3.666666667 + 4 = 0.333333333 4 + 4x + x2 = 0.333333333 Factor a perfect square on the left side: ((x) + 2)((x) + 2) = 0.333333333 Calculate the square root of the right side: 0.577350269 Break this problem into two subproblems by setting ((x) + 2) equal to 0.577350269 and -0.577350269.Subproblem 1
(x) + 2 = 0.577350269 Simplifying (x) + 2 = 0.577350269 x + 2 = 0.577350269 Reorder the terms: 2 + x = 0.577350269 Solving 2 + x = 0.577350269 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 = 0.577350269 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0.577350269 + -2 x = 0.577350269 + -2 Combine like terms: 0.577350269 + -2 = -1.422649731 x = -1.422649731 Simplifying x = -1.422649731Subproblem 2
(x) + 2 = -0.577350269 Simplifying (x) + 2 = -0.577350269 x + 2 = -0.577350269 Reorder the terms: 2 + x = -0.577350269 Solving 2 + x = -0.577350269 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 = -0.577350269 + -2 Combine like terms: 2 + -2 = 0 0 + x = -0.577350269 + -2 x = -0.577350269 + -2 Combine like terms: -0.577350269 + -2 = -2.577350269 x = -2.577350269 Simplifying x = -2.577350269Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.422649731, -2.577350269}
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