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Simplifying (3y * y + -7y + 4) = 1 Multiply y * y (3y2 + -7y + 4) = 1 Reorder the terms: (4 + -7y + 3y2) = 1 Remove parenthesis around (4 + -7y + 3y2) 4 + -7y + 3y2 = 1 Solving 4 + -7y + 3y2 = 1 Solving for variable 'y'. Reorder the terms: 4 + -1 + -7y + 3y2 = 1 + -1 Combine like terms: 4 + -1 = 3 3 + -7y + 3y2 = 1 + -1 Combine like terms: 1 + -1 = 0 3 + -7y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1 + -2.333333333y + y2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -2.333333333y + -1 + y2 = 0 + -1 Reorder the terms: 1 + -1 + -2.333333333y + y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2.333333333y + y2 = 0 + -1 -2.333333333y + y2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2.333333333y + y2 = -1 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 = -1 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333y + y2 = -1 + 1.361111112 Combine like terms: -1 + 1.361111112 = 0.361111112 1.361111112 + -2.333333333y + y2 = 0.361111112 Factor a perfect square on the left side: (y + -1.166666667)(y + -1.166666667) = 0.361111112 Calculate the square root of the right side: 0.600925213 Break this problem into two subproblems by setting (y + -1.166666667) equal to 0.600925213 and -0.600925213.Subproblem 1
y + -1.166666667 = 0.600925213 Simplifying y + -1.166666667 = 0.600925213 Reorder the terms: -1.166666667 + y = 0.600925213 Solving -1.166666667 + y = 0.600925213 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 = 0.600925213 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + y = 0.600925213 + 1.166666667 y = 0.600925213 + 1.166666667 Combine like terms: 0.600925213 + 1.166666667 = 1.76759188 y = 1.76759188 Simplifying y = 1.76759188Subproblem 2
y + -1.166666667 = -0.600925213 Simplifying y + -1.166666667 = -0.600925213 Reorder the terms: -1.166666667 + y = -0.600925213 Solving -1.166666667 + y = -0.600925213 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 = -0.600925213 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + y = -0.600925213 + 1.166666667 y = -0.600925213 + 1.166666667 Combine like terms: -0.600925213 + 1.166666667 = 0.565741454 y = 0.565741454 Simplifying y = 0.565741454Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.76759188, 0.565741454}
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