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Simplifying 2.1y2 + -3.5y = 4 Reorder the terms: -3.5y + 2.1y2 = 4 Solving -3.5y + 2.1y2 = 4 Solving for variable 'y'. Reorder the terms: -4 + -3.5y + 2.1y2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -3.5y + 2.1y2 = 0 Begin completing the square. Divide all terms by 2.1 the coefficient of the squared term: Divide each side by '2.1'. -1.904761905 + -1.666666667y + y2 = 0 Move the constant term to the right: Add '1.904761905' to each side of the equation. -1.904761905 + -1.666666667y + 1.904761905 + y2 = 0 + 1.904761905 Reorder the terms: -1.904761905 + 1.904761905 + -1.666666667y + y2 = 0 + 1.904761905 Combine like terms: -1.904761905 + 1.904761905 = 0.000000000 0.000000000 + -1.666666667y + y2 = 0 + 1.904761905 -1.666666667y + y2 = 0 + 1.904761905 Combine like terms: 0 + 1.904761905 = 1.904761905 -1.666666667y + y2 = 1.904761905 The y term is -1.666666667y. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667y + 0.6944444447 + y2 = 1.904761905 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667y + y2 = 1.904761905 + 0.6944444447 Combine like terms: 1.904761905 + 0.6944444447 = 2.5992063497 0.6944444447 + -1.666666667y + y2 = 2.5992063497 Factor a perfect square on the left side: (y + -0.8333333335)(y + -0.8333333335) = 2.5992063497 Calculate the square root of the right side: 1.61220543 Break this problem into two subproblems by setting (y + -0.8333333335) equal to 1.61220543 and -1.61220543.Subproblem 1
y + -0.8333333335 = 1.61220543 Simplifying y + -0.8333333335 = 1.61220543 Reorder the terms: -0.8333333335 + y = 1.61220543 Solving -0.8333333335 + y = 1.61220543 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + y = 1.61220543 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + y = 1.61220543 + 0.8333333335 y = 1.61220543 + 0.8333333335 Combine like terms: 1.61220543 + 0.8333333335 = 2.4455387635 y = 2.4455387635 Simplifying y = 2.4455387635Subproblem 2
y + -0.8333333335 = -1.61220543 Simplifying y + -0.8333333335 = -1.61220543 Reorder the terms: -0.8333333335 + y = -1.61220543 Solving -0.8333333335 + y = -1.61220543 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + y = -1.61220543 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + y = -1.61220543 + 0.8333333335 y = -1.61220543 + 0.8333333335 Combine like terms: -1.61220543 + 0.8333333335 = -0.7788720965 y = -0.7788720965 Simplifying y = -0.7788720965Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.4455387635, -0.7788720965}
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