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Simplifying 3y2 + 7y + -18 = 0 Reorder the terms: -18 + 7y + 3y2 = 0 Solving -18 + 7y + 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'. -6 + 2.333333333y + y2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 2.333333333y + 6 + y2 = 0 + 6 Reorder the terms: -6 + 6 + 2.333333333y + y2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 2.333333333y + y2 = 0 + 6 2.333333333y + y2 = 0 + 6 Combine like terms: 0 + 6 = 6 2.333333333y + y2 = 6 The y term is 2.333333333y. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333y + 1.361111112 + y2 = 6 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333y + y2 = 6 + 1.361111112 Combine like terms: 6 + 1.361111112 = 7.361111112 1.361111112 + 2.333333333y + y2 = 7.361111112 Factor a perfect square on the left side: (y + 1.166666667)(y + 1.166666667) = 7.361111112 Calculate the square root of the right side: 2.713136766 Break this problem into two subproblems by setting (y + 1.166666667) equal to 2.713136766 and -2.713136766.Subproblem 1
y + 1.166666667 = 2.713136766 Simplifying y + 1.166666667 = 2.713136766 Reorder the terms: 1.166666667 + y = 2.713136766 Solving 1.166666667 + y = 2.713136766 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + y = 2.713136766 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + y = 2.713136766 + -1.166666667 y = 2.713136766 + -1.166666667 Combine like terms: 2.713136766 + -1.166666667 = 1.546470099 y = 1.546470099 Simplifying y = 1.546470099Subproblem 2
y + 1.166666667 = -2.713136766 Simplifying y + 1.166666667 = -2.713136766 Reorder the terms: 1.166666667 + y = -2.713136766 Solving 1.166666667 + y = -2.713136766 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + y = -2.713136766 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + y = -2.713136766 + -1.166666667 y = -2.713136766 + -1.166666667 Combine like terms: -2.713136766 + -1.166666667 = -3.879803433 y = -3.879803433 Simplifying y = -3.879803433Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.546470099, -3.879803433}
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