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Simplifying 5y2 + 6y + -140 = 0 Reorder the terms: -140 + 6y + 5y2 = 0 Solving -140 + 6y + 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'. -28 + 1.2y + y2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + 1.2y + 28 + y2 = 0 + 28 Reorder the terms: -28 + 28 + 1.2y + y2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 1.2y + y2 = 0 + 28 1.2y + y2 = 0 + 28 Combine like terms: 0 + 28 = 28 1.2y + y2 = 28 The y term is 1.2y. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2y + 0.36 + y2 = 28 + 0.36 Reorder the terms: 0.36 + 1.2y + y2 = 28 + 0.36 Combine like terms: 28 + 0.36 = 28.36 0.36 + 1.2y + y2 = 28.36 Factor a perfect square on the left side: (y + 0.6)(y + 0.6) = 28.36 Calculate the square root of the right side: 5.325410782 Break this problem into two subproblems by setting (y + 0.6) equal to 5.325410782 and -5.325410782.Subproblem 1
y + 0.6 = 5.325410782 Simplifying y + 0.6 = 5.325410782 Reorder the terms: 0.6 + y = 5.325410782 Solving 0.6 + y = 5.325410782 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + y = 5.325410782 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + y = 5.325410782 + -0.6 y = 5.325410782 + -0.6 Combine like terms: 5.325410782 + -0.6 = 4.725410782 y = 4.725410782 Simplifying y = 4.725410782Subproblem 2
y + 0.6 = -5.325410782 Simplifying y + 0.6 = -5.325410782 Reorder the terms: 0.6 + y = -5.325410782 Solving 0.6 + y = -5.325410782 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + y = -5.325410782 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + y = -5.325410782 + -0.6 y = -5.325410782 + -0.6 Combine like terms: -5.325410782 + -0.6 = -5.925410782 y = -5.925410782 Simplifying y = -5.925410782Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.725410782, -5.925410782}
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