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Simplifying (7x + 3)(5x + 9) = 360 Reorder the terms: (3 + 7x)(5x + 9) = 360 Reorder the terms: (3 + 7x)(9 + 5x) = 360 Multiply (3 + 7x) * (9 + 5x) (3(9 + 5x) + 7x * (9 + 5x)) = 360 ((9 * 3 + 5x * 3) + 7x * (9 + 5x)) = 360 ((27 + 15x) + 7x * (9 + 5x)) = 360 (27 + 15x + (9 * 7x + 5x * 7x)) = 360 (27 + 15x + (63x + 35x2)) = 360 Combine like terms: 15x + 63x = 78x (27 + 78x + 35x2) = 360 Solving 27 + 78x + 35x2 = 360 Solving for variable 'x'. Reorder the terms: 27 + -360 + 78x + 35x2 = 360 + -360 Combine like terms: 27 + -360 = -333 -333 + 78x + 35x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -333 + 78x + 35x2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -9.514285714 + 2.228571429x + x2 = 0 Move the constant term to the right: Add '9.514285714' to each side of the equation. -9.514285714 + 2.228571429x + 9.514285714 + x2 = 0 + 9.514285714 Reorder the terms: -9.514285714 + 9.514285714 + 2.228571429x + x2 = 0 + 9.514285714 Combine like terms: -9.514285714 + 9.514285714 = 0.000000000 0.000000000 + 2.228571429x + x2 = 0 + 9.514285714 2.228571429x + x2 = 0 + 9.514285714 Combine like terms: 0 + 9.514285714 = 9.514285714 2.228571429x + x2 = 9.514285714 The x term is 2.228571429x. Take half its coefficient (1.114285715). Square it (1.241632655) and add it to both sides. Add '1.241632655' to each side of the equation. 2.228571429x + 1.241632655 + x2 = 9.514285714 + 1.241632655 Reorder the terms: 1.241632655 + 2.228571429x + x2 = 9.514285714 + 1.241632655 Combine like terms: 9.514285714 + 1.241632655 = 10.755918369 1.241632655 + 2.228571429x + x2 = 10.755918369 Factor a perfect square on the left side: (x + 1.114285715)(x + 1.114285715) = 10.755918369 Calculate the square root of the right side: 3.279621681 Break this problem into two subproblems by setting (x + 1.114285715) equal to 3.279621681 and -3.279621681.Subproblem 1
x + 1.114285715 = 3.279621681 Simplifying x + 1.114285715 = 3.279621681 Reorder the terms: 1.114285715 + x = 3.279621681 Solving 1.114285715 + x = 3.279621681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.114285715' to each side of the equation. 1.114285715 + -1.114285715 + x = 3.279621681 + -1.114285715 Combine like terms: 1.114285715 + -1.114285715 = 0.000000000 0.000000000 + x = 3.279621681 + -1.114285715 x = 3.279621681 + -1.114285715 Combine like terms: 3.279621681 + -1.114285715 = 2.165335966 x = 2.165335966 Simplifying x = 2.165335966Subproblem 2
x + 1.114285715 = -3.279621681 Simplifying x + 1.114285715 = -3.279621681 Reorder the terms: 1.114285715 + x = -3.279621681 Solving 1.114285715 + x = -3.279621681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.114285715' to each side of the equation. 1.114285715 + -1.114285715 + x = -3.279621681 + -1.114285715 Combine like terms: 1.114285715 + -1.114285715 = 0.000000000 0.000000000 + x = -3.279621681 + -1.114285715 x = -3.279621681 + -1.114285715 Combine like terms: -3.279621681 + -1.114285715 = -4.393907396 x = -4.393907396 Simplifying x = -4.393907396Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.165335966, -4.393907396}
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