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Simplifying -5y2 + 3y + 9 = 0 Reorder the terms: 9 + 3y + -5y2 = 0 Solving 9 + 3y + -5y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.8 + -0.6y + y2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + -0.6y + 1.8 + y2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + -0.6y + y2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + -0.6y + y2 = 0 + 1.8 -0.6y + y2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 -0.6y + y2 = 1.8 The y term is -0.6y. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6y + 0.09 + y2 = 1.8 + 0.09 Reorder the terms: 0.09 + -0.6y + y2 = 1.8 + 0.09 Combine like terms: 1.8 + 0.09 = 1.89 0.09 + -0.6y + y2 = 1.89 Factor a perfect square on the left side: (y + -0.3)(y + -0.3) = 1.89 Calculate the square root of the right side: 1.374772708 Break this problem into two subproblems by setting (y + -0.3) equal to 1.374772708 and -1.374772708.Subproblem 1
y + -0.3 = 1.374772708 Simplifying y + -0.3 = 1.374772708 Reorder the terms: -0.3 + y = 1.374772708 Solving -0.3 + y = 1.374772708 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + y = 1.374772708 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + y = 1.374772708 + 0.3 y = 1.374772708 + 0.3 Combine like terms: 1.374772708 + 0.3 = 1.674772708 y = 1.674772708 Simplifying y = 1.674772708Subproblem 2
y + -0.3 = -1.374772708 Simplifying y + -0.3 = -1.374772708 Reorder the terms: -0.3 + y = -1.374772708 Solving -0.3 + y = -1.374772708 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + y = -1.374772708 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + y = -1.374772708 + 0.3 y = -1.374772708 + 0.3 Combine like terms: -1.374772708 + 0.3 = -1.074772708 y = -1.074772708 Simplifying y = -1.074772708Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.674772708, -1.074772708}
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