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Simplifying 19y2 + -48y + 30 = 0 Reorder the terms: 30 + -48y + 19y2 = 0 Solving 30 + -48y + 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'. 1.578947368 + -2.526315789y + y2 = 0 Move the constant term to the right: Add '-1.578947368' to each side of the equation. 1.578947368 + -2.526315789y + -1.578947368 + y2 = 0 + -1.578947368 Reorder the terms: 1.578947368 + -1.578947368 + -2.526315789y + y2 = 0 + -1.578947368 Combine like terms: 1.578947368 + -1.578947368 = 0.000000000 0.000000000 + -2.526315789y + y2 = 0 + -1.578947368 -2.526315789y + y2 = 0 + -1.578947368 Combine like terms: 0 + -1.578947368 = -1.578947368 -2.526315789y + y2 = -1.578947368 The y term is -2.526315789y. Take half its coefficient (-1.263157895). Square it (1.595567868) and add it to both sides. Add '1.595567868' to each side of the equation. -2.526315789y + 1.595567868 + y2 = -1.578947368 + 1.595567868 Reorder the terms: 1.595567868 + -2.526315789y + y2 = -1.578947368 + 1.595567868 Combine like terms: -1.578947368 + 1.595567868 = 0.0166205 1.595567868 + -2.526315789y + y2 = 0.0166205 Factor a perfect square on the left side: (y + -1.263157895)(y + -1.263157895) = 0.0166205 Calculate the square root of the right side: 0.128920518 Break this problem into two subproblems by setting (y + -1.263157895) equal to 0.128920518 and -0.128920518.Subproblem 1
y + -1.263157895 = 0.128920518 Simplifying y + -1.263157895 = 0.128920518 Reorder the terms: -1.263157895 + y = 0.128920518 Solving -1.263157895 + y = 0.128920518 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.263157895' to each side of the equation. -1.263157895 + 1.263157895 + y = 0.128920518 + 1.263157895 Combine like terms: -1.263157895 + 1.263157895 = 0.000000000 0.000000000 + y = 0.128920518 + 1.263157895 y = 0.128920518 + 1.263157895 Combine like terms: 0.128920518 + 1.263157895 = 1.392078413 y = 1.392078413 Simplifying y = 1.392078413Subproblem 2
y + -1.263157895 = -0.128920518 Simplifying y + -1.263157895 = -0.128920518 Reorder the terms: -1.263157895 + y = -0.128920518 Solving -1.263157895 + y = -0.128920518 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.263157895' to each side of the equation. -1.263157895 + 1.263157895 + y = -0.128920518 + 1.263157895 Combine like terms: -1.263157895 + 1.263157895 = 0.000000000 0.000000000 + y = -0.128920518 + 1.263157895 y = -0.128920518 + 1.263157895 Combine like terms: -0.128920518 + 1.263157895 = 1.134237377 y = 1.134237377 Simplifying y = 1.134237377Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.392078413, 1.134237377}
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