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Simplifying 4y2 + y2 + -3y + -6 + 14y2 + -2 + 4y + -7y = 0 Reorder the terms: -6 + -2 + -3y + 4y + -7y + 4y2 + y2 + 14y2 = 0 Combine like terms: -6 + -2 = -8 -8 + -3y + 4y + -7y + 4y2 + y2 + 14y2 = 0 Combine like terms: -3y + 4y = 1y -8 + 1y + -7y + 4y2 + y2 + 14y2 = 0 Combine like terms: 1y + -7y = -6y -8 + -6y + 4y2 + y2 + 14y2 = 0 Combine like terms: 4y2 + y2 = 5y2 -8 + -6y + 5y2 + 14y2 = 0 Combine like terms: 5y2 + 14y2 = 19y2 -8 + -6y + 19y2 = 0 Solving -8 + -6y + 19y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. -0.4210526316 + -0.3157894737y + y2 = 0 Move the constant term to the right: Add '0.4210526316' to each side of the equation. -0.4210526316 + -0.3157894737y + 0.4210526316 + y2 = 0 + 0.4210526316 Reorder the terms: -0.4210526316 + 0.4210526316 + -0.3157894737y + y2 = 0 + 0.4210526316 Combine like terms: -0.4210526316 + 0.4210526316 = 0.0000000000 0.0000000000 + -0.3157894737y + y2 = 0 + 0.4210526316 -0.3157894737y + y2 = 0 + 0.4210526316 Combine like terms: 0 + 0.4210526316 = 0.4210526316 -0.3157894737y + y2 = 0.4210526316 The y term is -0.3157894737y. Take half its coefficient (-0.1578947369). Square it (0.02493074794) and add it to both sides. Add '0.02493074794' to each side of the equation. -0.3157894737y + 0.02493074794 + y2 = 0.4210526316 + 0.02493074794 Reorder the terms: 0.02493074794 + -0.3157894737y + y2 = 0.4210526316 + 0.02493074794 Combine like terms: 0.4210526316 + 0.02493074794 = 0.44598337954 0.02493074794 + -0.3157894737y + y2 = 0.44598337954 Factor a perfect square on the left side: (y + -0.1578947369)(y + -0.1578947369) = 0.44598337954 Calculate the square root of the right side: 0.667819871 Break this problem into two subproblems by setting (y + -0.1578947369) equal to 0.667819871 and -0.667819871.Subproblem 1
y + -0.1578947369 = 0.667819871 Simplifying y + -0.1578947369 = 0.667819871 Reorder the terms: -0.1578947369 + y = 0.667819871 Solving -0.1578947369 + y = 0.667819871 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1578947369' to each side of the equation. -0.1578947369 + 0.1578947369 + y = 0.667819871 + 0.1578947369 Combine like terms: -0.1578947369 + 0.1578947369 = 0.0000000000 0.0000000000 + y = 0.667819871 + 0.1578947369 y = 0.667819871 + 0.1578947369 Combine like terms: 0.667819871 + 0.1578947369 = 0.8257146079 y = 0.8257146079 Simplifying y = 0.8257146079Subproblem 2
y + -0.1578947369 = -0.667819871 Simplifying y + -0.1578947369 = -0.667819871 Reorder the terms: -0.1578947369 + y = -0.667819871 Solving -0.1578947369 + y = -0.667819871 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1578947369' to each side of the equation. -0.1578947369 + 0.1578947369 + y = -0.667819871 + 0.1578947369 Combine like terms: -0.1578947369 + 0.1578947369 = 0.0000000000 0.0000000000 + y = -0.667819871 + 0.1578947369 y = -0.667819871 + 0.1578947369 Combine like terms: -0.667819871 + 0.1578947369 = -0.5099251341 y = -0.5099251341 Simplifying y = -0.5099251341Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.8257146079, -0.5099251341}
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