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Simplifying 10y2 + 28y + -5 = 0 Reorder the terms: -5 + 28y + 10y2 = 0 Solving -5 + 28y + 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'. -0.5 + 2.8y + y2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 2.8y + 0.5 + y2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 2.8y + y2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 2.8y + y2 = 0 + 0.5 2.8y + y2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 2.8y + y2 = 0.5 The y term is 2.8y. Take half its coefficient (1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. 2.8y + 1.96 + y2 = 0.5 + 1.96 Reorder the terms: 1.96 + 2.8y + y2 = 0.5 + 1.96 Combine like terms: 0.5 + 1.96 = 2.46 1.96 + 2.8y + y2 = 2.46 Factor a perfect square on the left side: (y + 1.4)(y + 1.4) = 2.46 Calculate the square root of the right side: 1.568438714 Break this problem into two subproblems by setting (y + 1.4) equal to 1.568438714 and -1.568438714.Subproblem 1
y + 1.4 = 1.568438714 Simplifying y + 1.4 = 1.568438714 Reorder the terms: 1.4 + y = 1.568438714 Solving 1.4 + y = 1.568438714 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + y = 1.568438714 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + y = 1.568438714 + -1.4 y = 1.568438714 + -1.4 Combine like terms: 1.568438714 + -1.4 = 0.168438714 y = 0.168438714 Simplifying y = 0.168438714Subproblem 2
y + 1.4 = -1.568438714 Simplifying y + 1.4 = -1.568438714 Reorder the terms: 1.4 + y = -1.568438714 Solving 1.4 + y = -1.568438714 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + y = -1.568438714 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + y = -1.568438714 + -1.4 y = -1.568438714 + -1.4 Combine like terms: -1.568438714 + -1.4 = -2.968438714 y = -2.968438714 Simplifying y = -2.968438714Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.168438714, -2.968438714}
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