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Simplifying 6x2 + -12x + -48 = 80 Reorder the terms: -48 + -12x + 6x2 = 80 Solving -48 + -12x + 6x2 = 80 Solving for variable 'x'. Reorder the terms: -48 + -80 + -12x + 6x2 = 80 + -80 Combine like terms: -48 + -80 = -128 -128 + -12x + 6x2 = 80 + -80 Combine like terms: 80 + -80 = 0 -128 + -12x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-64 + -6x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-64 + -6x + 3x2)' equal to zero and attempt to solve: Simplifying -64 + -6x + 3x2 = 0 Solving -64 + -6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -21.33333333 + -2x + x2 = 0 Move the constant term to the right: Add '21.33333333' to each side of the equation. -21.33333333 + -2x + 21.33333333 + x2 = 0 + 21.33333333 Reorder the terms: -21.33333333 + 21.33333333 + -2x + x2 = 0 + 21.33333333 Combine like terms: -21.33333333 + 21.33333333 = 0.00000000 0.00000000 + -2x + x2 = 0 + 21.33333333 -2x + x2 = 0 + 21.33333333 Combine like terms: 0 + 21.33333333 = 21.33333333 -2x + x2 = 21.33333333 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 = 21.33333333 + 1 Reorder the terms: 1 + -2x + x2 = 21.33333333 + 1 Combine like terms: 21.33333333 + 1 = 22.33333333 1 + -2x + x2 = 22.33333333 Factor a perfect square on the left side: (x + -1)(x + -1) = 22.33333333 Calculate the square root of the right side: 4.725815626 Break this problem into two subproblems by setting (x + -1) equal to 4.725815626 and -4.725815626.Subproblem 1
x + -1 = 4.725815626 Simplifying x + -1 = 4.725815626 Reorder the terms: -1 + x = 4.725815626 Solving -1 + x = 4.725815626 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 = 4.725815626 + 1 Combine like terms: -1 + 1 = 0 0 + x = 4.725815626 + 1 x = 4.725815626 + 1 Combine like terms: 4.725815626 + 1 = 5.725815626 x = 5.725815626 Simplifying x = 5.725815626Subproblem 2
x + -1 = -4.725815626 Simplifying x + -1 = -4.725815626 Reorder the terms: -1 + x = -4.725815626 Solving -1 + x = -4.725815626 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 = -4.725815626 + 1 Combine like terms: -1 + 1 = 0 0 + x = -4.725815626 + 1 x = -4.725815626 + 1 Combine like terms: -4.725815626 + 1 = -3.725815626 x = -3.725815626 Simplifying x = -3.725815626Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.725815626, -3.725815626}Solution
x = {5.725815626, -3.725815626}
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