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Simplifying (3x + 6)(3x + 10) = 64 Reorder the terms: (6 + 3x)(3x + 10) = 64 Reorder the terms: (6 + 3x)(10 + 3x) = 64 Multiply (6 + 3x) * (10 + 3x) (6(10 + 3x) + 3x * (10 + 3x)) = 64 ((10 * 6 + 3x * 6) + 3x * (10 + 3x)) = 64 ((60 + 18x) + 3x * (10 + 3x)) = 64 (60 + 18x + (10 * 3x + 3x * 3x)) = 64 (60 + 18x + (30x + 9x2)) = 64 Combine like terms: 18x + 30x = 48x (60 + 48x + 9x2) = 64 Solving 60 + 48x + 9x2 = 64 Solving for variable 'x'. Reorder the terms: 60 + -64 + 48x + 9x2 = 64 + -64 Combine like terms: 60 + -64 = -4 -4 + 48x + 9x2 = 64 + -64 Combine like terms: 64 + -64 = 0 -4 + 48x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.4444444444 + 5.333333333x + x2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + 5.333333333x + 0.4444444444 + x2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + 5.333333333x + x2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + 5.333333333x + x2 = 0 + 0.4444444444 5.333333333x + x2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 5.333333333x + x2 = 0.4444444444 The x term is 5.333333333x. Take half its coefficient (2.666666667). Square it (7.111111113) and add it to both sides. Add '7.111111113' to each side of the equation. 5.333333333x + 7.111111113 + x2 = 0.4444444444 + 7.111111113 Reorder the terms: 7.111111113 + 5.333333333x + x2 = 0.4444444444 + 7.111111113 Combine like terms: 0.4444444444 + 7.111111113 = 7.5555555574 7.111111113 + 5.333333333x + x2 = 7.5555555574 Factor a perfect square on the left side: (x + 2.666666667)(x + 2.666666667) = 7.5555555574 Calculate the square root of the right side: 2.748737084 Break this problem into two subproblems by setting (x + 2.666666667) equal to 2.748737084 and -2.748737084.Subproblem 1
x + 2.666666667 = 2.748737084 Simplifying x + 2.666666667 = 2.748737084 Reorder the terms: 2.666666667 + x = 2.748737084 Solving 2.666666667 + x = 2.748737084 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.666666667' to each side of the equation. 2.666666667 + -2.666666667 + x = 2.748737084 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + x = 2.748737084 + -2.666666667 x = 2.748737084 + -2.666666667 Combine like terms: 2.748737084 + -2.666666667 = 0.082070417 x = 0.082070417 Simplifying x = 0.082070417Subproblem 2
x + 2.666666667 = -2.748737084 Simplifying x + 2.666666667 = -2.748737084 Reorder the terms: 2.666666667 + x = -2.748737084 Solving 2.666666667 + x = -2.748737084 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.666666667' to each side of the equation. 2.666666667 + -2.666666667 + x = -2.748737084 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + x = -2.748737084 + -2.666666667 x = -2.748737084 + -2.666666667 Combine like terms: -2.748737084 + -2.666666667 = -5.415403751 x = -5.415403751 Simplifying x = -5.415403751Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.082070417, -5.415403751}
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