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Simplifying -5y2 + 3y = -12 Reorder the terms: 3y + -5y2 = -12 Solving 3y + -5y2 = -12 Solving for variable 'y'. Reorder the terms: 12 + 3y + -5y2 = -12 + 12 Combine like terms: -12 + 12 = 0 12 + 3y + -5y2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -2.4 + -0.6y + y2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -0.6y + 2.4 + y2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -0.6y + y2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -0.6y + y2 = 0 + 2.4 -0.6y + y2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -0.6y + y2 = 2.4 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 = 2.4 + 0.09 Reorder the terms: 0.09 + -0.6y + y2 = 2.4 + 0.09 Combine like terms: 2.4 + 0.09 = 2.49 0.09 + -0.6y + y2 = 2.49 Factor a perfect square on the left side: (y + -0.3)(y + -0.3) = 2.49 Calculate the square root of the right side: 1.577973384 Break this problem into two subproblems by setting (y + -0.3) equal to 1.577973384 and -1.577973384.Subproblem 1
y + -0.3 = 1.577973384 Simplifying y + -0.3 = 1.577973384 Reorder the terms: -0.3 + y = 1.577973384 Solving -0.3 + y = 1.577973384 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 = 1.577973384 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + y = 1.577973384 + 0.3 y = 1.577973384 + 0.3 Combine like terms: 1.577973384 + 0.3 = 1.877973384 y = 1.877973384 Simplifying y = 1.877973384Subproblem 2
y + -0.3 = -1.577973384 Simplifying y + -0.3 = -1.577973384 Reorder the terms: -0.3 + y = -1.577973384 Solving -0.3 + y = -1.577973384 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 = -1.577973384 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + y = -1.577973384 + 0.3 y = -1.577973384 + 0.3 Combine like terms: -1.577973384 + 0.3 = -1.277973384 y = -1.277973384 Simplifying y = -1.277973384Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.877973384, -1.277973384}
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