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Simplifying 0 = -3x2 + 12x + -11 Reorder the terms: 0 = -11 + 12x + -3x2 Solving 0 = -11 + 12x + -3x2 Solving for variable 'x'. Combine like terms: 0 + 11 = 11 11 + -12x + 3x2 = -11 + 12x + -3x2 + 11 + -12x + 3x2 Reorder the terms: 11 + -12x + 3x2 = -11 + 11 + 12x + -12x + -3x2 + 3x2 Combine like terms: -11 + 11 = 0 11 + -12x + 3x2 = 0 + 12x + -12x + -3x2 + 3x2 11 + -12x + 3x2 = 12x + -12x + -3x2 + 3x2 Combine like terms: 12x + -12x = 0 11 + -12x + 3x2 = 0 + -3x2 + 3x2 11 + -12x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 11 + -12x + 3x2 = 0 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 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 = 2.577350269Subproblem 2
x + -2 = -0.577350269 Simplifying 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 = 1.422649731Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.577350269, 1.422649731}
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