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Simplifying 5y2 + -52y + 14 = 0 Reorder the terms: 14 + -52y + 5y2 = 0 Solving 14 + -52y + 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'. 2.8 + -10.4y + y2 = 0 Move the constant term to the right: Add '-2.8' to each side of the equation. 2.8 + -10.4y + -2.8 + y2 = 0 + -2.8 Reorder the terms: 2.8 + -2.8 + -10.4y + y2 = 0 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + -10.4y + y2 = 0 + -2.8 -10.4y + y2 = 0 + -2.8 Combine like terms: 0 + -2.8 = -2.8 -10.4y + y2 = -2.8 The y term is -10.4y. Take half its coefficient (-5.2). Square it (27.04) and add it to both sides. Add '27.04' to each side of the equation. -10.4y + 27.04 + y2 = -2.8 + 27.04 Reorder the terms: 27.04 + -10.4y + y2 = -2.8 + 27.04 Combine like terms: -2.8 + 27.04 = 24.24 27.04 + -10.4y + y2 = 24.24 Factor a perfect square on the left side: (y + -5.2)(y + -5.2) = 24.24 Calculate the square root of the right side: 4.92341345 Break this problem into two subproblems by setting (y + -5.2) equal to 4.92341345 and -4.92341345.Subproblem 1
y + -5.2 = 4.92341345 Simplifying y + -5.2 = 4.92341345 Reorder the terms: -5.2 + y = 4.92341345 Solving -5.2 + y = 4.92341345 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.2' to each side of the equation. -5.2 + 5.2 + y = 4.92341345 + 5.2 Combine like terms: -5.2 + 5.2 = 0.0 0.0 + y = 4.92341345 + 5.2 y = 4.92341345 + 5.2 Combine like terms: 4.92341345 + 5.2 = 10.12341345 y = 10.12341345 Simplifying y = 10.12341345Subproblem 2
y + -5.2 = -4.92341345 Simplifying y + -5.2 = -4.92341345 Reorder the terms: -5.2 + y = -4.92341345 Solving -5.2 + y = -4.92341345 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.2' to each side of the equation. -5.2 + 5.2 + y = -4.92341345 + 5.2 Combine like terms: -5.2 + 5.2 = 0.0 0.0 + y = -4.92341345 + 5.2 y = -4.92341345 + 5.2 Combine like terms: -4.92341345 + 5.2 = 0.27658655 y = 0.27658655 Simplifying y = 0.27658655Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.12341345, 0.27658655}
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