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Simplifying 5y2 + -18y + -12 = 0 Reorder the terms: -12 + -18y + 5y2 = 0 Solving -12 + -18y + 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'. -2.4 + -3.6y + y2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -3.6y + 2.4 + y2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -3.6y + y2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -3.6y + y2 = 0 + 2.4 -3.6y + y2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -3.6y + y2 = 2.4 The y term is -3.6y. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6y + 3.24 + y2 = 2.4 + 3.24 Reorder the terms: 3.24 + -3.6y + y2 = 2.4 + 3.24 Combine like terms: 2.4 + 3.24 = 5.64 3.24 + -3.6y + y2 = 5.64 Factor a perfect square on the left side: (y + -1.8)(y + -1.8) = 5.64 Calculate the square root of the right side: 2.374868417 Break this problem into two subproblems by setting (y + -1.8) equal to 2.374868417 and -2.374868417.Subproblem 1
y + -1.8 = 2.374868417 Simplifying y + -1.8 = 2.374868417 Reorder the terms: -1.8 + y = 2.374868417 Solving -1.8 + y = 2.374868417 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + y = 2.374868417 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + y = 2.374868417 + 1.8 y = 2.374868417 + 1.8 Combine like terms: 2.374868417 + 1.8 = 4.174868417 y = 4.174868417 Simplifying y = 4.174868417Subproblem 2
y + -1.8 = -2.374868417 Simplifying y + -1.8 = -2.374868417 Reorder the terms: -1.8 + y = -2.374868417 Solving -1.8 + y = -2.374868417 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + y = -2.374868417 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + y = -2.374868417 + 1.8 y = -2.374868417 + 1.8 Combine like terms: -2.374868417 + 1.8 = -0.574868417 y = -0.574868417 Simplifying y = -0.574868417Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.174868417, -0.574868417}
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