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Simplifying 10y2 + -4y = 45 Reorder the terms: -4y + 10y2 = 45 Solving -4y + 10y2 = 45 Solving for variable 'y'. Reorder the terms: -45 + -4y + 10y2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + -4y + 10y2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -4.5 + -0.4y + y2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -0.4y + 4.5 + y2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -0.4y + y2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -0.4y + y2 = 0 + 4.5 -0.4y + y2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -0.4y + y2 = 4.5 The y term is -0.4y. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4y + 0.04 + y2 = 4.5 + 0.04 Reorder the terms: 0.04 + -0.4y + y2 = 4.5 + 0.04 Combine like terms: 4.5 + 0.04 = 4.54 0.04 + -0.4y + y2 = 4.54 Factor a perfect square on the left side: (y + -0.2)(y + -0.2) = 4.54 Calculate the square root of the right side: 2.130727575 Break this problem into two subproblems by setting (y + -0.2) equal to 2.130727575 and -2.130727575.Subproblem 1
y + -0.2 = 2.130727575 Simplifying y + -0.2 = 2.130727575 Reorder the terms: -0.2 + y = 2.130727575 Solving -0.2 + y = 2.130727575 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + y = 2.130727575 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + y = 2.130727575 + 0.2 y = 2.130727575 + 0.2 Combine like terms: 2.130727575 + 0.2 = 2.330727575 y = 2.330727575 Simplifying y = 2.330727575Subproblem 2
y + -0.2 = -2.130727575 Simplifying y + -0.2 = -2.130727575 Reorder the terms: -0.2 + y = -2.130727575 Solving -0.2 + y = -2.130727575 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + y = -2.130727575 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + y = -2.130727575 + 0.2 y = -2.130727575 + 0.2 Combine like terms: -2.130727575 + 0.2 = -1.930727575 y = -1.930727575 Simplifying y = -1.930727575Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.330727575, -1.930727575}
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