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Simplifying 4y2 + -6y + -19 = 0 Reorder the terms: -19 + -6y + 4y2 = 0 Solving -19 + -6y + 4y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.75 + -1.5y + y2 = 0 Move the constant term to the right: Add '4.75' to each side of the equation. -4.75 + -1.5y + 4.75 + y2 = 0 + 4.75 Reorder the terms: -4.75 + 4.75 + -1.5y + y2 = 0 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + -1.5y + y2 = 0 + 4.75 -1.5y + y2 = 0 + 4.75 Combine like terms: 0 + 4.75 = 4.75 -1.5y + y2 = 4.75 The y term is -1.5y. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5y + 0.5625 + y2 = 4.75 + 0.5625 Reorder the terms: 0.5625 + -1.5y + y2 = 4.75 + 0.5625 Combine like terms: 4.75 + 0.5625 = 5.3125 0.5625 + -1.5y + y2 = 5.3125 Factor a perfect square on the left side: (y + -0.75)(y + -0.75) = 5.3125 Calculate the square root of the right side: 2.304886114 Break this problem into two subproblems by setting (y + -0.75) equal to 2.304886114 and -2.304886114.Subproblem 1
y + -0.75 = 2.304886114 Simplifying y + -0.75 = 2.304886114 Reorder the terms: -0.75 + y = 2.304886114 Solving -0.75 + y = 2.304886114 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + y = 2.304886114 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + y = 2.304886114 + 0.75 y = 2.304886114 + 0.75 Combine like terms: 2.304886114 + 0.75 = 3.054886114 y = 3.054886114 Simplifying y = 3.054886114Subproblem 2
y + -0.75 = -2.304886114 Simplifying y + -0.75 = -2.304886114 Reorder the terms: -0.75 + y = -2.304886114 Solving -0.75 + y = -2.304886114 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + y = -2.304886114 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + y = -2.304886114 + 0.75 y = -2.304886114 + 0.75 Combine like terms: -2.304886114 + 0.75 = -1.554886114 y = -1.554886114 Simplifying y = -1.554886114Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.054886114, -1.554886114}
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