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Simplifying 34y2 + 2y + -75 = 0 Reorder the terms: -75 + 2y + 34y2 = 0 Solving -75 + 2y + 34y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 34 the coefficient of the squared term: Divide each side by '34'. -2.205882353 + 0.05882352941y + y2 = 0 Move the constant term to the right: Add '2.205882353' to each side of the equation. -2.205882353 + 0.05882352941y + 2.205882353 + y2 = 0 + 2.205882353 Reorder the terms: -2.205882353 + 2.205882353 + 0.05882352941y + y2 = 0 + 2.205882353 Combine like terms: -2.205882353 + 2.205882353 = 0.000000000 0.000000000 + 0.05882352941y + y2 = 0 + 2.205882353 0.05882352941y + y2 = 0 + 2.205882353 Combine like terms: 0 + 2.205882353 = 2.205882353 0.05882352941y + y2 = 2.205882353 The y term is 0.05882352941y. Take half its coefficient (0.02941176471). Square it (0.0008650519034) and add it to both sides. Add '0.0008650519034' to each side of the equation. 0.05882352941y + 0.0008650519034 + y2 = 2.205882353 + 0.0008650519034 Reorder the terms: 0.0008650519034 + 0.05882352941y + y2 = 2.205882353 + 0.0008650519034 Combine like terms: 2.205882353 + 0.0008650519034 = 2.2067474049034 0.0008650519034 + 0.05882352941y + y2 = 2.2067474049034 Factor a perfect square on the left side: (y + 0.02941176471)(y + 0.02941176471) = 2.2067474049034 Calculate the square root of the right side: 1.485512506 Break this problem into two subproblems by setting (y + 0.02941176471) equal to 1.485512506 and -1.485512506.Subproblem 1
y + 0.02941176471 = 1.485512506 Simplifying y + 0.02941176471 = 1.485512506 Reorder the terms: 0.02941176471 + y = 1.485512506 Solving 0.02941176471 + y = 1.485512506 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.02941176471' to each side of the equation. 0.02941176471 + -0.02941176471 + y = 1.485512506 + -0.02941176471 Combine like terms: 0.02941176471 + -0.02941176471 = 0.00000000000 0.00000000000 + y = 1.485512506 + -0.02941176471 y = 1.485512506 + -0.02941176471 Combine like terms: 1.485512506 + -0.02941176471 = 1.45610074129 y = 1.45610074129 Simplifying y = 1.45610074129Subproblem 2
y + 0.02941176471 = -1.485512506 Simplifying y + 0.02941176471 = -1.485512506 Reorder the terms: 0.02941176471 + y = -1.485512506 Solving 0.02941176471 + y = -1.485512506 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.02941176471' to each side of the equation. 0.02941176471 + -0.02941176471 + y = -1.485512506 + -0.02941176471 Combine like terms: 0.02941176471 + -0.02941176471 = 0.00000000000 0.00000000000 + y = -1.485512506 + -0.02941176471 y = -1.485512506 + -0.02941176471 Combine like terms: -1.485512506 + -0.02941176471 = -1.51492427071 y = -1.51492427071 Simplifying y = -1.51492427071Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.45610074129, -1.51492427071}
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