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Simplifying -6x2 + -44x = 18 Reorder the terms: -44x + -6x2 = 18 Solving -44x + -6x2 = 18 Solving for variable 'x'. Reorder the terms: -18 + -44x + -6x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + -44x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(9 + 22x + 3x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(9 + 22x + 3x2)' equal to zero and attempt to solve: Simplifying 9 + 22x + 3x2 = 0 Solving 9 + 22x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3 + 7.333333333x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 7.333333333x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 7.333333333x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 7.333333333x + x2 = 0 + -3 7.333333333x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 7.333333333x + x2 = -3 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 = -3 + 13.44444445 Reorder the terms: 13.44444445 + 7.333333333x + x2 = -3 + 13.44444445 Combine like terms: -3 + 13.44444445 = 10.44444445 13.44444445 + 7.333333333x + x2 = 10.44444445 Factor a perfect square on the left side: (x + 3.666666667)(x + 3.666666667) = 10.44444445 Calculate the square root of the right side: 3.231786572 Break this problem into two subproblems by setting (x + 3.666666667) equal to 3.231786572 and -3.231786572.Subproblem 1
x + 3.666666667 = 3.231786572 Simplifying x + 3.666666667 = 3.231786572 Reorder the terms: 3.666666667 + x = 3.231786572 Solving 3.666666667 + x = 3.231786572 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 = 3.231786572 + -3.666666667 Combine like terms: 3.666666667 + -3.666666667 = 0.000000000 0.000000000 + x = 3.231786572 + -3.666666667 x = 3.231786572 + -3.666666667 Combine like terms: 3.231786572 + -3.666666667 = -0.434880095 x = -0.434880095 Simplifying x = -0.434880095Subproblem 2
x + 3.666666667 = -3.231786572 Simplifying x + 3.666666667 = -3.231786572 Reorder the terms: 3.666666667 + x = -3.231786572 Solving 3.666666667 + x = -3.231786572 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 = -3.231786572 + -3.666666667 Combine like terms: 3.666666667 + -3.666666667 = 0.000000000 0.000000000 + x = -3.231786572 + -3.666666667 x = -3.231786572 + -3.666666667 Combine like terms: -3.231786572 + -3.666666667 = -6.898453239 x = -6.898453239 Simplifying x = -6.898453239Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.434880095, -6.898453239}Solution
x = {-0.434880095, -6.898453239}
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