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Simplifying 119y2 + -162y + -945 = 0 Reorder the terms: -945 + -162y + 119y2 = 0 Solving -945 + -162y + 119y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 119 the coefficient of the squared term: Divide each side by '119'. -7.941176471 + -1.361344538y + y2 = 0 Move the constant term to the right: Add '7.941176471' to each side of the equation. -7.941176471 + -1.361344538y + 7.941176471 + y2 = 0 + 7.941176471 Reorder the terms: -7.941176471 + 7.941176471 + -1.361344538y + y2 = 0 + 7.941176471 Combine like terms: -7.941176471 + 7.941176471 = 0.000000000 0.000000000 + -1.361344538y + y2 = 0 + 7.941176471 -1.361344538y + y2 = 0 + 7.941176471 Combine like terms: 0 + 7.941176471 = 7.941176471 -1.361344538y + y2 = 7.941176471 The y term is -1.361344538y. Take half its coefficient (-0.680672269). Square it (0.4633147378) and add it to both sides. Add '0.4633147378' to each side of the equation. -1.361344538y + 0.4633147378 + y2 = 7.941176471 + 0.4633147378 Reorder the terms: 0.4633147378 + -1.361344538y + y2 = 7.941176471 + 0.4633147378 Combine like terms: 7.941176471 + 0.4633147378 = 8.4044912088 0.4633147378 + -1.361344538y + y2 = 8.4044912088 Factor a perfect square on the left side: (y + -0.680672269)(y + -0.680672269) = 8.4044912088 Calculate the square root of the right side: 2.899050053 Break this problem into two subproblems by setting (y + -0.680672269) equal to 2.899050053 and -2.899050053.Subproblem 1
y + -0.680672269 = 2.899050053 Simplifying y + -0.680672269 = 2.899050053 Reorder the terms: -0.680672269 + y = 2.899050053 Solving -0.680672269 + y = 2.899050053 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.680672269' to each side of the equation. -0.680672269 + 0.680672269 + y = 2.899050053 + 0.680672269 Combine like terms: -0.680672269 + 0.680672269 = 0.000000000 0.000000000 + y = 2.899050053 + 0.680672269 y = 2.899050053 + 0.680672269 Combine like terms: 2.899050053 + 0.680672269 = 3.579722322 y = 3.579722322 Simplifying y = 3.579722322Subproblem 2
y + -0.680672269 = -2.899050053 Simplifying y + -0.680672269 = -2.899050053 Reorder the terms: -0.680672269 + y = -2.899050053 Solving -0.680672269 + y = -2.899050053 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.680672269' to each side of the equation. -0.680672269 + 0.680672269 + y = -2.899050053 + 0.680672269 Combine like terms: -0.680672269 + 0.680672269 = 0.000000000 0.000000000 + y = -2.899050053 + 0.680672269 y = -2.899050053 + 0.680672269 Combine like terms: -2.899050053 + 0.680672269 = -2.218377784 y = -2.218377784 Simplifying y = -2.218377784Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.579722322, -2.218377784}
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