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Simplifying 6x2 + -44x + -144 = 0 Reorder the terms: -144 + -44x + 6x2 = 0 Solving -144 + -44x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-72 + -22x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-72 + -22x + 3x2)' equal to zero and attempt to solve: Simplifying -72 + -22x + 3x2 = 0 Solving -72 + -22x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -24 + -7.333333333x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + -7.333333333x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -7.333333333x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -7.333333333x + x2 = 0 + 24 -7.333333333x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -7.333333333x + x2 = 24 The x term is -7.333333333x. Take half its coefficient (-3.666666667). Square it (13.44444445) and add it to both sides. Add '13.44444445' to each side of the equation. -7.333333333x + 13.44444445 + x2 = 24 + 13.44444445 Reorder the terms: 13.44444445 + -7.333333333x + x2 = 24 + 13.44444445 Combine like terms: 24 + 13.44444445 = 37.44444445 13.44444445 + -7.333333333x + x2 = 37.44444445 Factor a perfect square on the left side: (x + -3.666666667)(x + -3.666666667) = 37.44444445 Calculate the square root of the right side: 6.119186584 Break this problem into two subproblems by setting (x + -3.666666667) equal to 6.119186584 and -6.119186584.Subproblem 1
x + -3.666666667 = 6.119186584 Simplifying x + -3.666666667 = 6.119186584 Reorder the terms: -3.666666667 + x = 6.119186584 Solving -3.666666667 + x = 6.119186584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.666666667' to each side of the equation. -3.666666667 + 3.666666667 + x = 6.119186584 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + x = 6.119186584 + 3.666666667 x = 6.119186584 + 3.666666667 Combine like terms: 6.119186584 + 3.666666667 = 9.785853251 x = 9.785853251 Simplifying x = 9.785853251Subproblem 2
x + -3.666666667 = -6.119186584 Simplifying x + -3.666666667 = -6.119186584 Reorder the terms: -3.666666667 + x = -6.119186584 Solving -3.666666667 + x = -6.119186584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.666666667' to each side of the equation. -3.666666667 + 3.666666667 + x = -6.119186584 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + x = -6.119186584 + 3.666666667 x = -6.119186584 + 3.666666667 Combine like terms: -6.119186584 + 3.666666667 = -2.452519917 x = -2.452519917 Simplifying x = -2.452519917Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.785853251, -2.452519917}Solution
x = {9.785853251, -2.452519917}
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