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Simplifying 12x2 + -24x + -40 = 0 Reorder the terms: -40 + -24x + 12x2 = 0 Solving -40 + -24x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-10 + -6x + 3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-10 + -6x + 3x2)' equal to zero and attempt to solve: Simplifying -10 + -6x + 3x2 = 0 Solving -10 + -6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.333333333 + -2x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + -2x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + -2x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + -2x + x2 = 0 + 3.333333333 -2x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 -2x + x2 = 3.333333333 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 3.333333333 + 1 Reorder the terms: 1 + -2x + x2 = 3.333333333 + 1 Combine like terms: 3.333333333 + 1 = 4.333333333 1 + -2x + x2 = 4.333333333 Factor a perfect square on the left side: (x + -1)(x + -1) = 4.333333333 Calculate the square root of the right side: 2.081665999 Break this problem into two subproblems by setting (x + -1) equal to 2.081665999 and -2.081665999.Subproblem 1
x + -1 = 2.081665999 Simplifying x + -1 = 2.081665999 Reorder the terms: -1 + x = 2.081665999 Solving -1 + x = 2.081665999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.081665999 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.081665999 + 1 x = 2.081665999 + 1 Combine like terms: 2.081665999 + 1 = 3.081665999 x = 3.081665999 Simplifying x = 3.081665999Subproblem 2
x + -1 = -2.081665999 Simplifying x + -1 = -2.081665999 Reorder the terms: -1 + x = -2.081665999 Solving -1 + x = -2.081665999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.081665999 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.081665999 + 1 x = -2.081665999 + 1 Combine like terms: -2.081665999 + 1 = -1.081665999 x = -1.081665999 Simplifying x = -1.081665999Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.081665999, -1.081665999}Solution
x = {3.081665999, -1.081665999}
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