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Simplifying 21y2 + 10y + -19 = 0 Reorder the terms: -19 + 10y + 21y2 = 0 Solving -19 + 10y + 21y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -0.9047619048 + 0.4761904762y + y2 = 0 Move the constant term to the right: Add '0.9047619048' to each side of the equation. -0.9047619048 + 0.4761904762y + 0.9047619048 + y2 = 0 + 0.9047619048 Reorder the terms: -0.9047619048 + 0.9047619048 + 0.4761904762y + y2 = 0 + 0.9047619048 Combine like terms: -0.9047619048 + 0.9047619048 = 0.0000000000 0.0000000000 + 0.4761904762y + y2 = 0 + 0.9047619048 0.4761904762y + y2 = 0 + 0.9047619048 Combine like terms: 0 + 0.9047619048 = 0.9047619048 0.4761904762y + y2 = 0.9047619048 The y term is 0.4761904762y. Take half its coefficient (0.2380952381). Square it (0.05668934241) and add it to both sides. Add '0.05668934241' to each side of the equation. 0.4761904762y + 0.05668934241 + y2 = 0.9047619048 + 0.05668934241 Reorder the terms: 0.05668934241 + 0.4761904762y + y2 = 0.9047619048 + 0.05668934241 Combine like terms: 0.9047619048 + 0.05668934241 = 0.96145124721 0.05668934241 + 0.4761904762y + y2 = 0.96145124721 Factor a perfect square on the left side: (y + 0.2380952381)(y + 0.2380952381) = 0.96145124721 Calculate the square root of the right side: 0.980536204 Break this problem into two subproblems by setting (y + 0.2380952381) equal to 0.980536204 and -0.980536204.Subproblem 1
y + 0.2380952381 = 0.980536204 Simplifying y + 0.2380952381 = 0.980536204 Reorder the terms: 0.2380952381 + y = 0.980536204 Solving 0.2380952381 + y = 0.980536204 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.2380952381' to each side of the equation. 0.2380952381 + -0.2380952381 + y = 0.980536204 + -0.2380952381 Combine like terms: 0.2380952381 + -0.2380952381 = 0.0000000000 0.0000000000 + y = 0.980536204 + -0.2380952381 y = 0.980536204 + -0.2380952381 Combine like terms: 0.980536204 + -0.2380952381 = 0.7424409659 y = 0.7424409659 Simplifying y = 0.7424409659Subproblem 2
y + 0.2380952381 = -0.980536204 Simplifying y + 0.2380952381 = -0.980536204 Reorder the terms: 0.2380952381 + y = -0.980536204 Solving 0.2380952381 + y = -0.980536204 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.2380952381' to each side of the equation. 0.2380952381 + -0.2380952381 + y = -0.980536204 + -0.2380952381 Combine like terms: 0.2380952381 + -0.2380952381 = 0.0000000000 0.0000000000 + y = -0.980536204 + -0.2380952381 y = -0.980536204 + -0.2380952381 Combine like terms: -0.980536204 + -0.2380952381 = -1.2186314421 y = -1.2186314421 Simplifying y = -1.2186314421Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.7424409659, -1.2186314421}
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