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Simplifying 0.333y2 = y + 0.1666 Reorder the terms: 0.333y2 = 0.1666 + y Solving 0.333y2 = 0.1666 + y Solving for variable 'y'. Reorder the terms: -0.1666 + -1y + 0.333y2 = 0.1666 + y + -0.1666 + -1y Reorder the terms: -0.1666 + -1y + 0.333y2 = 0.1666 + -0.1666 + y + -1y Combine like terms: 0.1666 + -0.1666 = 0.0000 -0.1666 + -1y + 0.333y2 = 0.0000 + y + -1y -0.1666 + -1y + 0.333y2 = y + -1y Combine like terms: y + -1y = 0 -0.1666 + -1y + 0.333y2 = 0 Begin completing the square. Divide all terms by 0.333 the coefficient of the squared term: Divide each side by '0.333'. -0.5003003003 + -3.003003003y + y2 = 0 Move the constant term to the right: Add '0.5003003003' to each side of the equation. -0.5003003003 + -3.003003003y + 0.5003003003 + y2 = 0 + 0.5003003003 Reorder the terms: -0.5003003003 + 0.5003003003 + -3.003003003y + y2 = 0 + 0.5003003003 Combine like terms: -0.5003003003 + 0.5003003003 = 0.0000000000 0.0000000000 + -3.003003003y + y2 = 0 + 0.5003003003 -3.003003003y + y2 = 0 + 0.5003003003 Combine like terms: 0 + 0.5003003003 = 0.5003003003 -3.003003003y + y2 = 0.5003003003 The y term is -3.003003003y. Take half its coefficient (-1.501501502). Square it (2.254506761) and add it to both sides. Add '2.254506761' to each side of the equation. -3.003003003y + 2.254506761 + y2 = 0.5003003003 + 2.254506761 Reorder the terms: 2.254506761 + -3.003003003y + y2 = 0.5003003003 + 2.254506761 Combine like terms: 0.5003003003 + 2.254506761 = 2.7548070613 2.254506761 + -3.003003003y + y2 = 2.7548070613 Factor a perfect square on the left side: (y + -1.501501502)(y + -1.501501502) = 2.7548070613 Calculate the square root of the right side: 1.659761146 Break this problem into two subproblems by setting (y + -1.501501502) equal to 1.659761146 and -1.659761146.Subproblem 1
y + -1.501501502 = 1.659761146 Simplifying y + -1.501501502 = 1.659761146 Reorder the terms: -1.501501502 + y = 1.659761146 Solving -1.501501502 + y = 1.659761146 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.501501502' to each side of the equation. -1.501501502 + 1.501501502 + y = 1.659761146 + 1.501501502 Combine like terms: -1.501501502 + 1.501501502 = 0.000000000 0.000000000 + y = 1.659761146 + 1.501501502 y = 1.659761146 + 1.501501502 Combine like terms: 1.659761146 + 1.501501502 = 3.161262648 y = 3.161262648 Simplifying y = 3.161262648Subproblem 2
y + -1.501501502 = -1.659761146 Simplifying y + -1.501501502 = -1.659761146 Reorder the terms: -1.501501502 + y = -1.659761146 Solving -1.501501502 + y = -1.659761146 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.501501502' to each side of the equation. -1.501501502 + 1.501501502 + y = -1.659761146 + 1.501501502 Combine like terms: -1.501501502 + 1.501501502 = 0.000000000 0.000000000 + y = -1.659761146 + 1.501501502 y = -1.659761146 + 1.501501502 Combine like terms: -1.659761146 + 1.501501502 = -0.158259644 y = -0.158259644 Simplifying y = -0.158259644Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.161262648, -0.158259644}
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