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Simplifying 3y2 + 5y + -150 = 0 Reorder the terms: -150 + 5y + 3y2 = 0 Solving -150 + 5y + 3y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -50 + 1.666666667y + y2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + 1.666666667y + 50 + y2 = 0 + 50 Reorder the terms: -50 + 50 + 1.666666667y + y2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 1.666666667y + y2 = 0 + 50 1.666666667y + y2 = 0 + 50 Combine like terms: 0 + 50 = 50 1.666666667y + y2 = 50 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 = 50 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667y + y2 = 50 + 0.6944444447 Combine like terms: 50 + 0.6944444447 = 50.6944444447 0.6944444447 + 1.666666667y + y2 = 50.6944444447 Factor a perfect square on the left side: (y + 0.8333333335)(y + 0.8333333335) = 50.6944444447 Calculate the square root of the right side: 7.120003121 Break this problem into two subproblems by setting (y + 0.8333333335) equal to 7.120003121 and -7.120003121.Subproblem 1
y + 0.8333333335 = 7.120003121 Simplifying y + 0.8333333335 = 7.120003121 Reorder the terms: 0.8333333335 + y = 7.120003121 Solving 0.8333333335 + y = 7.120003121 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 = 7.120003121 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + y = 7.120003121 + -0.8333333335 y = 7.120003121 + -0.8333333335 Combine like terms: 7.120003121 + -0.8333333335 = 6.2866697875 y = 6.2866697875 Simplifying y = 6.2866697875Subproblem 2
y + 0.8333333335 = -7.120003121 Simplifying y + 0.8333333335 = -7.120003121 Reorder the terms: 0.8333333335 + y = -7.120003121 Solving 0.8333333335 + y = -7.120003121 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 = -7.120003121 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + y = -7.120003121 + -0.8333333335 y = -7.120003121 + -0.8333333335 Combine like terms: -7.120003121 + -0.8333333335 = -7.9533364545 y = -7.9533364545 Simplifying y = -7.9533364545Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.2866697875, -7.9533364545}
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