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Simplifying 10y2 + -79y + -154 = 0 Reorder the terms: -154 + -79y + 10y2 = 0 Solving -154 + -79y + 10y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -15.4 + -7.9y + y2 = 0 Move the constant term to the right: Add '15.4' to each side of the equation. -15.4 + -7.9y + 15.4 + y2 = 0 + 15.4 Reorder the terms: -15.4 + 15.4 + -7.9y + y2 = 0 + 15.4 Combine like terms: -15.4 + 15.4 = 0.0 0.0 + -7.9y + y2 = 0 + 15.4 -7.9y + y2 = 0 + 15.4 Combine like terms: 0 + 15.4 = 15.4 -7.9y + y2 = 15.4 The y term is -7.9y. Take half its coefficient (-3.95). Square it (15.6025) and add it to both sides. Add '15.6025' to each side of the equation. -7.9y + 15.6025 + y2 = 15.4 + 15.6025 Reorder the terms: 15.6025 + -7.9y + y2 = 15.4 + 15.6025 Combine like terms: 15.4 + 15.6025 = 31.0025 15.6025 + -7.9y + y2 = 31.0025 Factor a perfect square on the left side: (y + -3.95)(y + -3.95) = 31.0025 Calculate the square root of the right side: 5.567988865 Break this problem into two subproblems by setting (y + -3.95) equal to 5.567988865 and -5.567988865.Subproblem 1
y + -3.95 = 5.567988865 Simplifying y + -3.95 = 5.567988865 Reorder the terms: -3.95 + y = 5.567988865 Solving -3.95 + y = 5.567988865 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.95' to each side of the equation. -3.95 + 3.95 + y = 5.567988865 + 3.95 Combine like terms: -3.95 + 3.95 = 0.00 0.00 + y = 5.567988865 + 3.95 y = 5.567988865 + 3.95 Combine like terms: 5.567988865 + 3.95 = 9.517988865 y = 9.517988865 Simplifying y = 9.517988865Subproblem 2
y + -3.95 = -5.567988865 Simplifying y + -3.95 = -5.567988865 Reorder the terms: -3.95 + y = -5.567988865 Solving -3.95 + y = -5.567988865 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.95' to each side of the equation. -3.95 + 3.95 + y = -5.567988865 + 3.95 Combine like terms: -3.95 + 3.95 = 0.00 0.00 + y = -5.567988865 + 3.95 y = -5.567988865 + 3.95 Combine like terms: -5.567988865 + 3.95 = -1.617988865 y = -1.617988865 Simplifying y = -1.617988865Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.517988865, -1.617988865}
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