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Simplifying 9y(7y + -5) + -1(3y + 7) = 0 Reorder the terms: 9y(-5 + 7y) + -1(3y + 7) = 0 (-5 * 9y + 7y * 9y) + -1(3y + 7) = 0 (-45y + 63y2) + -1(3y + 7) = 0 Reorder the terms: -45y + 63y2 + -1(7 + 3y) = 0 -45y + 63y2 + (7 * -1 + 3y * -1) = 0 -45y + 63y2 + (-7 + -3y) = 0 Reorder the terms: -7 + -45y + -3y + 63y2 = 0 Combine like terms: -45y + -3y = -48y -7 + -48y + 63y2 = 0 Solving -7 + -48y + 63y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 63 the coefficient of the squared term: Divide each side by '63'. -0.1111111111 + -0.7619047619y + y2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + -0.7619047619y + 0.1111111111 + y2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + -0.7619047619y + y2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + -0.7619047619y + y2 = 0 + 0.1111111111 -0.7619047619y + y2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 -0.7619047619y + y2 = 0.1111111111 The y term is -0.7619047619y. Take half its coefficient (-0.380952381). Square it (0.1451247166) and add it to both sides. Add '0.1451247166' to each side of the equation. -0.7619047619y + 0.1451247166 + y2 = 0.1111111111 + 0.1451247166 Reorder the terms: 0.1451247166 + -0.7619047619y + y2 = 0.1111111111 + 0.1451247166 Combine like terms: 0.1111111111 + 0.1451247166 = 0.2562358277 0.1451247166 + -0.7619047619y + y2 = 0.2562358277 Factor a perfect square on the left side: (y + -0.380952381)(y + -0.380952381) = 0.2562358277 Calculate the square root of the right side: 0.50619742 Break this problem into two subproblems by setting (y + -0.380952381) equal to 0.50619742 and -0.50619742.Subproblem 1
y + -0.380952381 = 0.50619742 Simplifying y + -0.380952381 = 0.50619742 Reorder the terms: -0.380952381 + y = 0.50619742 Solving -0.380952381 + y = 0.50619742 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.380952381' to each side of the equation. -0.380952381 + 0.380952381 + y = 0.50619742 + 0.380952381 Combine like terms: -0.380952381 + 0.380952381 = 0.000000000 0.000000000 + y = 0.50619742 + 0.380952381 y = 0.50619742 + 0.380952381 Combine like terms: 0.50619742 + 0.380952381 = 0.887149801 y = 0.887149801 Simplifying y = 0.887149801Subproblem 2
y + -0.380952381 = -0.50619742 Simplifying y + -0.380952381 = -0.50619742 Reorder the terms: -0.380952381 + y = -0.50619742 Solving -0.380952381 + y = -0.50619742 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.380952381' to each side of the equation. -0.380952381 + 0.380952381 + y = -0.50619742 + 0.380952381 Combine like terms: -0.380952381 + 0.380952381 = 0.000000000 0.000000000 + y = -0.50619742 + 0.380952381 y = -0.50619742 + 0.380952381 Combine like terms: -0.50619742 + 0.380952381 = -0.125245039 y = -0.125245039 Simplifying y = -0.125245039Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.887149801, -0.125245039}
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