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Simplifying 21y2 + 46y + 20 = 0 Reorder the terms: 20 + 46y + 21y2 = 0 Solving 20 + 46y + 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'. 0.9523809524 + 2.19047619y + y2 = 0 Move the constant term to the right: Add '-0.9523809524' to each side of the equation. 0.9523809524 + 2.19047619y + -0.9523809524 + y2 = 0 + -0.9523809524 Reorder the terms: 0.9523809524 + -0.9523809524 + 2.19047619y + y2 = 0 + -0.9523809524 Combine like terms: 0.9523809524 + -0.9523809524 = 0.0000000000 0.0000000000 + 2.19047619y + y2 = 0 + -0.9523809524 2.19047619y + y2 = 0 + -0.9523809524 Combine like terms: 0 + -0.9523809524 = -0.9523809524 2.19047619y + y2 = -0.9523809524 The y term is 2.19047619y. Take half its coefficient (1.095238095). Square it (1.199546485) and add it to both sides. Add '1.199546485' to each side of the equation. 2.19047619y + 1.199546485 + y2 = -0.9523809524 + 1.199546485 Reorder the terms: 1.199546485 + 2.19047619y + y2 = -0.9523809524 + 1.199546485 Combine like terms: -0.9523809524 + 1.199546485 = 0.2471655326 1.199546485 + 2.19047619y + y2 = 0.2471655326 Factor a perfect square on the left side: (y + 1.095238095)(y + 1.095238095) = 0.2471655326 Calculate the square root of the right side: 0.497157453 Break this problem into two subproblems by setting (y + 1.095238095) equal to 0.497157453 and -0.497157453.Subproblem 1
y + 1.095238095 = 0.497157453 Simplifying y + 1.095238095 = 0.497157453 Reorder the terms: 1.095238095 + y = 0.497157453 Solving 1.095238095 + y = 0.497157453 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.095238095' to each side of the equation. 1.095238095 + -1.095238095 + y = 0.497157453 + -1.095238095 Combine like terms: 1.095238095 + -1.095238095 = 0.000000000 0.000000000 + y = 0.497157453 + -1.095238095 y = 0.497157453 + -1.095238095 Combine like terms: 0.497157453 + -1.095238095 = -0.598080642 y = -0.598080642 Simplifying y = -0.598080642Subproblem 2
y + 1.095238095 = -0.497157453 Simplifying y + 1.095238095 = -0.497157453 Reorder the terms: 1.095238095 + y = -0.497157453 Solving 1.095238095 + y = -0.497157453 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.095238095' to each side of the equation. 1.095238095 + -1.095238095 + y = -0.497157453 + -1.095238095 Combine like terms: 1.095238095 + -1.095238095 = 0.000000000 0.000000000 + y = -0.497157453 + -1.095238095 y = -0.497157453 + -1.095238095 Combine like terms: -0.497157453 + -1.095238095 = -1.592395548 y = -1.592395548 Simplifying y = -1.592395548Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.598080642, -1.592395548}
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