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Simplifying (3x + 4)(x + 9) = 53x + 39 Reorder the terms: (4 + 3x)(x + 9) = 53x + 39 Reorder the terms: (4 + 3x)(9 + x) = 53x + 39 Multiply (4 + 3x) * (9 + x) (4(9 + x) + 3x * (9 + x)) = 53x + 39 ((9 * 4 + x * 4) + 3x * (9 + x)) = 53x + 39 ((36 + 4x) + 3x * (9 + x)) = 53x + 39 (36 + 4x + (9 * 3x + x * 3x)) = 53x + 39 (36 + 4x + (27x + 3x2)) = 53x + 39 Combine like terms: 4x + 27x = 31x (36 + 31x + 3x2) = 53x + 39 Reorder the terms: 36 + 31x + 3x2 = 39 + 53x Solving 36 + 31x + 3x2 = 39 + 53x Solving for variable 'x'. Reorder the terms: 36 + -39 + 31x + -53x + 3x2 = 39 + 53x + -39 + -53x Combine like terms: 36 + -39 = -3 -3 + 31x + -53x + 3x2 = 39 + 53x + -39 + -53x Combine like terms: 31x + -53x = -22x -3 + -22x + 3x2 = 39 + 53x + -39 + -53x Reorder the terms: -3 + -22x + 3x2 = 39 + -39 + 53x + -53x Combine like terms: 39 + -39 = 0 -3 + -22x + 3x2 = 0 + 53x + -53x -3 + -22x + 3x2 = 53x + -53x Combine like terms: 53x + -53x = 0 -3 + -22x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1 + -7.333333333x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -7.333333333x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -7.333333333x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -7.333333333x + x2 = 0 + 1 -7.333333333x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -7.333333333x + x2 = 1 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 = 1 + 13.44444445 Reorder the terms: 13.44444445 + -7.333333333x + x2 = 1 + 13.44444445 Combine like terms: 1 + 13.44444445 = 14.44444445 13.44444445 + -7.333333333x + x2 = 14.44444445 Factor a perfect square on the left side: (x + -3.666666667)(x + -3.666666667) = 14.44444445 Calculate the square root of the right side: 3.800584751 Break this problem into two subproblems by setting (x + -3.666666667) equal to 3.800584751 and -3.800584751.Subproblem 1
x + -3.666666667 = 3.800584751 Simplifying x + -3.666666667 = 3.800584751 Reorder the terms: -3.666666667 + x = 3.800584751 Solving -3.666666667 + x = 3.800584751 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 = 3.800584751 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + x = 3.800584751 + 3.666666667 x = 3.800584751 + 3.666666667 Combine like terms: 3.800584751 + 3.666666667 = 7.467251418 x = 7.467251418 Simplifying x = 7.467251418Subproblem 2
x + -3.666666667 = -3.800584751 Simplifying x + -3.666666667 = -3.800584751 Reorder the terms: -3.666666667 + x = -3.800584751 Solving -3.666666667 + x = -3.800584751 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 = -3.800584751 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + x = -3.800584751 + 3.666666667 x = -3.800584751 + 3.666666667 Combine like terms: -3.800584751 + 3.666666667 = -0.133918084 x = -0.133918084 Simplifying x = -0.133918084Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.467251418, -0.133918084}
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