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Simplifying 3x2 + -12x = 11 Reorder the terms: -12x + 3x2 = 11 Solving -12x + 3x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + -12x + 3x2 = 11 + -11 Combine like terms: 11 + -11 = 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 = 7.666666667 4 + -4x + x2 = 7.666666667 Factor a perfect square on the left side: (x + -2)(x + -2) = 7.666666667 Calculate the square root of the right side: 2.768874621 Break this problem into two subproblems by setting (x + -2) equal to 2.768874621 and -2.768874621.Subproblem 1
x + -2 = 2.768874621 Simplifying x + -2 = 2.768874621 Reorder the terms: -2 + x = 2.768874621 Solving -2 + x = 2.768874621 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 = 2.768874621 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.768874621 + 2 x = 2.768874621 + 2 Combine like terms: 2.768874621 + 2 = 4.768874621 x = 4.768874621 Simplifying x = 4.768874621Subproblem 2
x + -2 = -2.768874621 Simplifying x + -2 = -2.768874621 Reorder the terms: -2 + x = -2.768874621 Solving -2 + x = -2.768874621 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 = -2.768874621 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.768874621 + 2 x = -2.768874621 + 2 Combine like terms: -2.768874621 + 2 = -0.768874621 x = -0.768874621 Simplifying x = -0.768874621Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.768874621, -0.768874621}
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