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Simplifying 5y2 + 4y = 14 Reorder the terms: 4y + 5y2 = 14 Solving 4y + 5y2 = 14 Solving for variable 'y'. Reorder the terms: -14 + 4y + 5y2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + 4y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.8 + 0.8y + y2 = 0 Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + 0.8y + 2.8 + y2 = 0 + 2.8 Reorder the terms: -2.8 + 2.8 + 0.8y + y2 = 0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + 0.8y + y2 = 0 + 2.8 0.8y + y2 = 0 + 2.8 Combine like terms: 0 + 2.8 = 2.8 0.8y + y2 = 2.8 The y term is 0.8y. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8y + 0.16 + y2 = 2.8 + 0.16 Reorder the terms: 0.16 + 0.8y + y2 = 2.8 + 0.16 Combine like terms: 2.8 + 0.16 = 2.96 0.16 + 0.8y + y2 = 2.96 Factor a perfect square on the left side: (y + 0.4)(y + 0.4) = 2.96 Calculate the square root of the right side: 1.720465053 Break this problem into two subproblems by setting (y + 0.4) equal to 1.720465053 and -1.720465053.Subproblem 1
y + 0.4 = 1.720465053 Simplifying y + 0.4 = 1.720465053 Reorder the terms: 0.4 + y = 1.720465053 Solving 0.4 + y = 1.720465053 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + y = 1.720465053 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + y = 1.720465053 + -0.4 y = 1.720465053 + -0.4 Combine like terms: 1.720465053 + -0.4 = 1.320465053 y = 1.320465053 Simplifying y = 1.320465053Subproblem 2
y + 0.4 = -1.720465053 Simplifying y + 0.4 = -1.720465053 Reorder the terms: 0.4 + y = -1.720465053 Solving 0.4 + y = -1.720465053 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + y = -1.720465053 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + y = -1.720465053 + -0.4 y = -1.720465053 + -0.4 Combine like terms: -1.720465053 + -0.4 = -2.120465053 y = -2.120465053 Simplifying y = -2.120465053Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.320465053, -2.120465053}
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