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Simplifying 19y2 + 32y + -10 = 0 Reorder the terms: -10 + 32y + 19y2 = 0 Solving -10 + 32y + 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'. -0.5263157895 + 1.684210526y + y2 = 0 Move the constant term to the right: Add '0.5263157895' to each side of the equation. -0.5263157895 + 1.684210526y + 0.5263157895 + y2 = 0 + 0.5263157895 Reorder the terms: -0.5263157895 + 0.5263157895 + 1.684210526y + y2 = 0 + 0.5263157895 Combine like terms: -0.5263157895 + 0.5263157895 = 0.0000000000 0.0000000000 + 1.684210526y + y2 = 0 + 0.5263157895 1.684210526y + y2 = 0 + 0.5263157895 Combine like terms: 0 + 0.5263157895 = 0.5263157895 1.684210526y + y2 = 0.5263157895 The y term is 1.684210526y. Take half its coefficient (0.842105263). Square it (0.7091412740) and add it to both sides. Add '0.7091412740' to each side of the equation. 1.684210526y + 0.7091412740 + y2 = 0.5263157895 + 0.7091412740 Reorder the terms: 0.7091412740 + 1.684210526y + y2 = 0.5263157895 + 0.7091412740 Combine like terms: 0.5263157895 + 0.7091412740 = 1.2354570635 0.7091412740 + 1.684210526y + y2 = 1.2354570635 Factor a perfect square on the left side: (y + 0.842105263)(y + 0.842105263) = 1.2354570635 Calculate the square root of the right side: 1.111511162 Break this problem into two subproblems by setting (y + 0.842105263) equal to 1.111511162 and -1.111511162.Subproblem 1
y + 0.842105263 = 1.111511162 Simplifying y + 0.842105263 = 1.111511162 Reorder the terms: 0.842105263 + y = 1.111511162 Solving 0.842105263 + y = 1.111511162 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.842105263' to each side of the equation. 0.842105263 + -0.842105263 + y = 1.111511162 + -0.842105263 Combine like terms: 0.842105263 + -0.842105263 = 0.000000000 0.000000000 + y = 1.111511162 + -0.842105263 y = 1.111511162 + -0.842105263 Combine like terms: 1.111511162 + -0.842105263 = 0.269405899 y = 0.269405899 Simplifying y = 0.269405899Subproblem 2
y + 0.842105263 = -1.111511162 Simplifying y + 0.842105263 = -1.111511162 Reorder the terms: 0.842105263 + y = -1.111511162 Solving 0.842105263 + y = -1.111511162 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.842105263' to each side of the equation. 0.842105263 + -0.842105263 + y = -1.111511162 + -0.842105263 Combine like terms: 0.842105263 + -0.842105263 = 0.000000000 0.000000000 + y = -1.111511162 + -0.842105263 y = -1.111511162 + -0.842105263 Combine like terms: -1.111511162 + -0.842105263 = -1.953616425 y = -1.953616425 Simplifying y = -1.953616425Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.269405899, -1.953616425}
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