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Simplifying 3y2 + 44y = 871 Reorder the terms: 44y + 3y2 = 871 Solving 44y + 3y2 = 871 Solving for variable 'y'. Reorder the terms: -871 + 44y + 3y2 = 871 + -871 Combine like terms: 871 + -871 = 0 -871 + 44y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -290.3333333 + 14.66666667y + y2 = 0 Move the constant term to the right: Add '290.3333333' to each side of the equation. -290.3333333 + 14.66666667y + 290.3333333 + y2 = 0 + 290.3333333 Reorder the terms: -290.3333333 + 290.3333333 + 14.66666667y + y2 = 0 + 290.3333333 Combine like terms: -290.3333333 + 290.3333333 = 0.0000000 0.0000000 + 14.66666667y + y2 = 0 + 290.3333333 14.66666667y + y2 = 0 + 290.3333333 Combine like terms: 0 + 290.3333333 = 290.3333333 14.66666667y + y2 = 290.3333333 The y term is 14.66666667y. Take half its coefficient (7.333333335). Square it (53.77777780) and add it to both sides. Add '53.77777780' to each side of the equation. 14.66666667y + 53.77777780 + y2 = 290.3333333 + 53.77777780 Reorder the terms: 53.77777780 + 14.66666667y + y2 = 290.3333333 + 53.77777780 Combine like terms: 290.3333333 + 53.77777780 = 344.1111111 53.77777780 + 14.66666667y + y2 = 344.1111111 Factor a perfect square on the left side: (y + 7.333333335)(y + 7.333333335) = 344.1111111 Calculate the square root of the right side: 18.550232104 Break this problem into two subproblems by setting (y + 7.333333335) equal to 18.550232104 and -18.550232104.Subproblem 1
y + 7.333333335 = 18.550232104 Simplifying y + 7.333333335 = 18.550232104 Reorder the terms: 7.333333335 + y = 18.550232104 Solving 7.333333335 + y = 18.550232104 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-7.333333335' to each side of the equation. 7.333333335 + -7.333333335 + y = 18.550232104 + -7.333333335 Combine like terms: 7.333333335 + -7.333333335 = 0.000000000 0.000000000 + y = 18.550232104 + -7.333333335 y = 18.550232104 + -7.333333335 Combine like terms: 18.550232104 + -7.333333335 = 11.216898769 y = 11.216898769 Simplifying y = 11.216898769Subproblem 2
y + 7.333333335 = -18.550232104 Simplifying y + 7.333333335 = -18.550232104 Reorder the terms: 7.333333335 + y = -18.550232104 Solving 7.333333335 + y = -18.550232104 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-7.333333335' to each side of the equation. 7.333333335 + -7.333333335 + y = -18.550232104 + -7.333333335 Combine like terms: 7.333333335 + -7.333333335 = 0.000000000 0.000000000 + y = -18.550232104 + -7.333333335 y = -18.550232104 + -7.333333335 Combine like terms: -18.550232104 + -7.333333335 = -25.883565439 y = -25.883565439 Simplifying y = -25.883565439Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.216898769, -25.883565439}
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