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Simplifying 19y2 + 41y + -9 = 0 Reorder the terms: -9 + 41y + 19y2 = 0 Solving -9 + 41y + 19y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. -0.4736842105 + 2.157894737y + y2 = 0 Move the constant term to the right: Add '0.4736842105' to each side of the equation. -0.4736842105 + 2.157894737y + 0.4736842105 + y2 = 0 + 0.4736842105 Reorder the terms: -0.4736842105 + 0.4736842105 + 2.157894737y + y2 = 0 + 0.4736842105 Combine like terms: -0.4736842105 + 0.4736842105 = 0.0000000000 0.0000000000 + 2.157894737y + y2 = 0 + 0.4736842105 2.157894737y + y2 = 0 + 0.4736842105 Combine like terms: 0 + 0.4736842105 = 0.4736842105 2.157894737y + y2 = 0.4736842105 The y term is 2.157894737y. Take half its coefficient (1.078947369). Square it (1.164127425) and add it to both sides. Add '1.164127425' to each side of the equation. 2.157894737y + 1.164127425 + y2 = 0.4736842105 + 1.164127425 Reorder the terms: 1.164127425 + 2.157894737y + y2 = 0.4736842105 + 1.164127425 Combine like terms: 0.4736842105 + 1.164127425 = 1.6378116355 1.164127425 + 2.157894737y + y2 = 1.6378116355 Factor a perfect square on the left side: (y + 1.078947369)(y + 1.078947369) = 1.6378116355 Calculate the square root of the right side: 1.279770149 Break this problem into two subproblems by setting (y + 1.078947369) equal to 1.279770149 and -1.279770149.Subproblem 1
y + 1.078947369 = 1.279770149 Simplifying y + 1.078947369 = 1.279770149 Reorder the terms: 1.078947369 + y = 1.279770149 Solving 1.078947369 + y = 1.279770149 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.078947369' to each side of the equation. 1.078947369 + -1.078947369 + y = 1.279770149 + -1.078947369 Combine like terms: 1.078947369 + -1.078947369 = 0.000000000 0.000000000 + y = 1.279770149 + -1.078947369 y = 1.279770149 + -1.078947369 Combine like terms: 1.279770149 + -1.078947369 = 0.20082278 y = 0.20082278 Simplifying y = 0.20082278Subproblem 2
y + 1.078947369 = -1.279770149 Simplifying y + 1.078947369 = -1.279770149 Reorder the terms: 1.078947369 + y = -1.279770149 Solving 1.078947369 + y = -1.279770149 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.078947369' to each side of the equation. 1.078947369 + -1.078947369 + y = -1.279770149 + -1.078947369 Combine like terms: 1.078947369 + -1.078947369 = 0.000000000 0.000000000 + y = -1.279770149 + -1.078947369 y = -1.279770149 + -1.078947369 Combine like terms: -1.279770149 + -1.078947369 = -2.358717518 y = -2.358717518 Simplifying y = -2.358717518Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.20082278, -2.358717518}
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