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Simplifying 5y2 + -51y + 18 = 0 Reorder the terms: 18 + -51y + 5y2 = 0 Solving 18 + -51y + 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'. 3.6 + -10.2y + y2 = 0 Move the constant term to the right: Add '-3.6' to each side of the equation. 3.6 + -10.2y + -3.6 + y2 = 0 + -3.6 Reorder the terms: 3.6 + -3.6 + -10.2y + y2 = 0 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + -10.2y + y2 = 0 + -3.6 -10.2y + y2 = 0 + -3.6 Combine like terms: 0 + -3.6 = -3.6 -10.2y + y2 = -3.6 The y term is -10.2y. Take half its coefficient (-5.1). Square it (26.01) and add it to both sides. Add '26.01' to each side of the equation. -10.2y + 26.01 + y2 = -3.6 + 26.01 Reorder the terms: 26.01 + -10.2y + y2 = -3.6 + 26.01 Combine like terms: -3.6 + 26.01 = 22.41 26.01 + -10.2y + y2 = 22.41 Factor a perfect square on the left side: (y + -5.1)(y + -5.1) = 22.41 Calculate the square root of the right side: 4.733920151 Break this problem into two subproblems by setting (y + -5.1) equal to 4.733920151 and -4.733920151.Subproblem 1
y + -5.1 = 4.733920151 Simplifying y + -5.1 = 4.733920151 Reorder the terms: -5.1 + y = 4.733920151 Solving -5.1 + y = 4.733920151 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.1' to each side of the equation. -5.1 + 5.1 + y = 4.733920151 + 5.1 Combine like terms: -5.1 + 5.1 = 0.0 0.0 + y = 4.733920151 + 5.1 y = 4.733920151 + 5.1 Combine like terms: 4.733920151 + 5.1 = 9.833920151 y = 9.833920151 Simplifying y = 9.833920151Subproblem 2
y + -5.1 = -4.733920151 Simplifying y + -5.1 = -4.733920151 Reorder the terms: -5.1 + y = -4.733920151 Solving -5.1 + y = -4.733920151 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.1' to each side of the equation. -5.1 + 5.1 + y = -4.733920151 + 5.1 Combine like terms: -5.1 + 5.1 = 0.0 0.0 + y = -4.733920151 + 5.1 y = -4.733920151 + 5.1 Combine like terms: -4.733920151 + 5.1 = 0.366079849 y = 0.366079849 Simplifying y = 0.366079849Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.833920151, 0.366079849}
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