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Simplifying 0 = 3x2 + -36x + -72 Reorder the terms: 0 = -72 + -36x + 3x2 Solving 0 = -72 + -36x + 3x2 Solving for variable 'x'. Combine like terms: 0 + 72 = 72 72 + 36x + -3x2 = -72 + -36x + 3x2 + 72 + 36x + -3x2 Reorder the terms: 72 + 36x + -3x2 = -72 + 72 + -36x + 36x + 3x2 + -3x2 Combine like terms: -72 + 72 = 0 72 + 36x + -3x2 = 0 + -36x + 36x + 3x2 + -3x2 72 + 36x + -3x2 = -36x + 36x + 3x2 + -3x2 Combine like terms: -36x + 36x = 0 72 + 36x + -3x2 = 0 + 3x2 + -3x2 72 + 36x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 72 + 36x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(24 + 12x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(24 + 12x + -1x2)' equal to zero and attempt to solve: Simplifying 24 + 12x + -1x2 = 0 Solving 24 + 12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -24 + -12x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + -12x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -12x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -12x + x2 = 0 + 24 -12x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -12x + x2 = 24 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 24 + 36 Reorder the terms: 36 + -12x + x2 = 24 + 36 Combine like terms: 24 + 36 = 60 36 + -12x + x2 = 60 Factor a perfect square on the left side: (x + -6)(x + -6) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (x + -6) equal to 7.745966692 and -7.745966692.Subproblem 1
x + -6 = 7.745966692 Simplifying x + -6 = 7.745966692 Reorder the terms: -6 + x = 7.745966692 Solving -6 + x = 7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 7.745966692 + 6 Combine like terms: -6 + 6 = 0 0 + x = 7.745966692 + 6 x = 7.745966692 + 6 Combine like terms: 7.745966692 + 6 = 13.745966692 x = 13.745966692 Simplifying x = 13.745966692Subproblem 2
x + -6 = -7.745966692 Simplifying x + -6 = -7.745966692 Reorder the terms: -6 + x = -7.745966692 Solving -6 + x = -7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -7.745966692 + 6 Combine like terms: -6 + 6 = 0 0 + x = -7.745966692 + 6 x = -7.745966692 + 6 Combine like terms: -7.745966692 + 6 = -1.745966692 x = -1.745966692 Simplifying x = -1.745966692Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.745966692, -1.745966692}Solution
x = {13.745966692, -1.745966692}
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