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Simplifying 6x2 + -6x + -72 = 45 Reorder the terms: -72 + -6x + 6x2 = 45 Solving -72 + -6x + 6x2 = 45 Solving for variable 'x'. Reorder the terms: -72 + -45 + -6x + 6x2 = 45 + -45 Combine like terms: -72 + -45 = -117 -117 + -6x + 6x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -117 + -6x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-39 + -2x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-39 + -2x + 2x2)' equal to zero and attempt to solve: Simplifying -39 + -2x + 2x2 = 0 Solving -39 + -2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -19.5 + -1x + x2 = 0 Move the constant term to the right: Add '19.5' to each side of the equation. -19.5 + -1x + 19.5 + x2 = 0 + 19.5 Reorder the terms: -19.5 + 19.5 + -1x + x2 = 0 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + -1x + x2 = 0 + 19.5 -1x + x2 = 0 + 19.5 Combine like terms: 0 + 19.5 = 19.5 -1x + x2 = 19.5 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 19.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 19.5 + 0.25 Combine like terms: 19.5 + 0.25 = 19.75 0.25 + -1x + x2 = 19.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 19.75 Calculate the square root of the right side: 4.444097209 Break this problem into two subproblems by setting (x + -0.5) equal to 4.444097209 and -4.444097209.Subproblem 1
x + -0.5 = 4.444097209 Simplifying x + -0.5 = 4.444097209 Reorder the terms: -0.5 + x = 4.444097209 Solving -0.5 + x = 4.444097209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 4.444097209 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 4.444097209 + 0.5 x = 4.444097209 + 0.5 Combine like terms: 4.444097209 + 0.5 = 4.944097209 x = 4.944097209 Simplifying x = 4.944097209Subproblem 2
x + -0.5 = -4.444097209 Simplifying x + -0.5 = -4.444097209 Reorder the terms: -0.5 + x = -4.444097209 Solving -0.5 + x = -4.444097209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -4.444097209 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -4.444097209 + 0.5 x = -4.444097209 + 0.5 Combine like terms: -4.444097209 + 0.5 = -3.944097209 x = -3.944097209 Simplifying x = -3.944097209Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.944097209, -3.944097209}Solution
x = {4.944097209, -3.944097209}
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