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Simplifying (7y + 9)(3y + 4) = 143 Reorder the terms: (9 + 7y)(3y + 4) = 143 Reorder the terms: (9 + 7y)(4 + 3y) = 143 Multiply (9 + 7y) * (4 + 3y) (9(4 + 3y) + 7y * (4 + 3y)) = 143 ((4 * 9 + 3y * 9) + 7y * (4 + 3y)) = 143 ((36 + 27y) + 7y * (4 + 3y)) = 143 (36 + 27y + (4 * 7y + 3y * 7y)) = 143 (36 + 27y + (28y + 21y2)) = 143 Combine like terms: 27y + 28y = 55y (36 + 55y + 21y2) = 143 Solving 36 + 55y + 21y2 = 143 Solving for variable 'y'. Reorder the terms: 36 + -143 + 55y + 21y2 = 143 + -143 Combine like terms: 36 + -143 = -107 -107 + 55y + 21y2 = 143 + -143 Combine like terms: 143 + -143 = 0 -107 + 55y + 21y2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -5.095238095 + 2.619047619y + y2 = 0 Move the constant term to the right: Add '5.095238095' to each side of the equation. -5.095238095 + 2.619047619y + 5.095238095 + y2 = 0 + 5.095238095 Reorder the terms: -5.095238095 + 5.095238095 + 2.619047619y + y2 = 0 + 5.095238095 Combine like terms: -5.095238095 + 5.095238095 = 0.000000000 0.000000000 + 2.619047619y + y2 = 0 + 5.095238095 2.619047619y + y2 = 0 + 5.095238095 Combine like terms: 0 + 5.095238095 = 5.095238095 2.619047619y + y2 = 5.095238095 The y term is 2.619047619y. Take half its coefficient (1.30952381). Square it (1.714852609) and add it to both sides. Add '1.714852609' to each side of the equation. 2.619047619y + 1.714852609 + y2 = 5.095238095 + 1.714852609 Reorder the terms: 1.714852609 + 2.619047619y + y2 = 5.095238095 + 1.714852609 Combine like terms: 5.095238095 + 1.714852609 = 6.810090704 1.714852609 + 2.619047619y + y2 = 6.810090704 Factor a perfect square on the left side: (y + 1.30952381)(y + 1.30952381) = 6.810090704 Calculate the square root of the right side: 2.609615049 Break this problem into two subproblems by setting (y + 1.30952381) equal to 2.609615049 and -2.609615049.Subproblem 1
y + 1.30952381 = 2.609615049 Simplifying y + 1.30952381 = 2.609615049 Reorder the terms: 1.30952381 + y = 2.609615049 Solving 1.30952381 + y = 2.609615049 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.30952381' to each side of the equation. 1.30952381 + -1.30952381 + y = 2.609615049 + -1.30952381 Combine like terms: 1.30952381 + -1.30952381 = 0.00000000 0.00000000 + y = 2.609615049 + -1.30952381 y = 2.609615049 + -1.30952381 Combine like terms: 2.609615049 + -1.30952381 = 1.300091239 y = 1.300091239 Simplifying y = 1.300091239Subproblem 2
y + 1.30952381 = -2.609615049 Simplifying y + 1.30952381 = -2.609615049 Reorder the terms: 1.30952381 + y = -2.609615049 Solving 1.30952381 + y = -2.609615049 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.30952381' to each side of the equation. 1.30952381 + -1.30952381 + y = -2.609615049 + -1.30952381 Combine like terms: 1.30952381 + -1.30952381 = 0.00000000 0.00000000 + y = -2.609615049 + -1.30952381 y = -2.609615049 + -1.30952381 Combine like terms: -2.609615049 + -1.30952381 = -3.919138859 y = -3.919138859 Simplifying y = -3.919138859Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.300091239, -3.919138859}
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