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Simplifying 18y2 + -7y + -2 = 0 Reorder the terms: -2 + -7y + 18y2 = 0 Solving -2 + -7y + 18y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.1111111111 + -0.3888888889y + y2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + -0.3888888889y + 0.1111111111 + y2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + -0.3888888889y + y2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + -0.3888888889y + y2 = 0 + 0.1111111111 -0.3888888889y + y2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 -0.3888888889y + y2 = 0.1111111111 The y term is -0.3888888889y. Take half its coefficient (-0.1944444445). Square it (0.03780864200) and add it to both sides. Add '0.03780864200' to each side of the equation. -0.3888888889y + 0.03780864200 + y2 = 0.1111111111 + 0.03780864200 Reorder the terms: 0.03780864200 + -0.3888888889y + y2 = 0.1111111111 + 0.03780864200 Combine like terms: 0.1111111111 + 0.03780864200 = 0.1489197531 0.03780864200 + -0.3888888889y + y2 = 0.1489197531 Factor a perfect square on the left side: (y + -0.1944444445)(y + -0.1944444445) = 0.1489197531 Calculate the square root of the right side: 0.385901222 Break this problem into two subproblems by setting (y + -0.1944444445) equal to 0.385901222 and -0.385901222.Subproblem 1
y + -0.1944444445 = 0.385901222 Simplifying y + -0.1944444445 = 0.385901222 Reorder the terms: -0.1944444445 + y = 0.385901222 Solving -0.1944444445 + y = 0.385901222 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1944444445' to each side of the equation. -0.1944444445 + 0.1944444445 + y = 0.385901222 + 0.1944444445 Combine like terms: -0.1944444445 + 0.1944444445 = 0.0000000000 0.0000000000 + y = 0.385901222 + 0.1944444445 y = 0.385901222 + 0.1944444445 Combine like terms: 0.385901222 + 0.1944444445 = 0.5803456665 y = 0.5803456665 Simplifying y = 0.5803456665Subproblem 2
y + -0.1944444445 = -0.385901222 Simplifying y + -0.1944444445 = -0.385901222 Reorder the terms: -0.1944444445 + y = -0.385901222 Solving -0.1944444445 + y = -0.385901222 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1944444445' to each side of the equation. -0.1944444445 + 0.1944444445 + y = -0.385901222 + 0.1944444445 Combine like terms: -0.1944444445 + 0.1944444445 = 0.0000000000 0.0000000000 + y = -0.385901222 + 0.1944444445 y = -0.385901222 + 0.1944444445 Combine like terms: -0.385901222 + 0.1944444445 = -0.1914567775 y = -0.1914567775 Simplifying y = -0.1914567775Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.5803456665, -0.1914567775}
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