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Simplifying 7 = y2 + -3y Reorder the terms: 7 = -3y + y2 Solving 7 = -3y + y2 Solving for variable 'y'. Reorder the terms: 7 + 3y + -1y2 = -3y + 3y + y2 + -1y2 Combine like terms: -3y + 3y = 0 7 + 3y + -1y2 = 0 + y2 + -1y2 7 + 3y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 7 + 3y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7 + -3y + y2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -3y + 7 + y2 = 0 + 7 Reorder the terms: -7 + 7 + -3y + y2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -3y + y2 = 0 + 7 -3y + y2 = 0 + 7 Combine like terms: 0 + 7 = 7 -3y + y2 = 7 The y term is -3y. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3y + 2.25 + y2 = 7 + 2.25 Reorder the terms: 2.25 + -3y + y2 = 7 + 2.25 Combine like terms: 7 + 2.25 = 9.25 2.25 + -3y + y2 = 9.25 Factor a perfect square on the left side: (y + -1.5)(y + -1.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (y + -1.5) equal to 3.041381265 and -3.041381265.Subproblem 1
y + -1.5 = 3.041381265 Simplifying y + -1.5 = 3.041381265 Reorder the terms: -1.5 + y = 3.041381265 Solving -1.5 + y = 3.041381265 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = 3.041381265 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = 3.041381265 + 1.5 y = 3.041381265 + 1.5 Combine like terms: 3.041381265 + 1.5 = 4.541381265 y = 4.541381265 Simplifying y = 4.541381265Subproblem 2
y + -1.5 = -3.041381265 Simplifying y + -1.5 = -3.041381265 Reorder the terms: -1.5 + y = -3.041381265 Solving -1.5 + y = -3.041381265 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = -3.041381265 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = -3.041381265 + 1.5 y = -3.041381265 + 1.5 Combine like terms: -3.041381265 + 1.5 = -1.541381265 y = -1.541381265 Simplifying y = -1.541381265Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.541381265, -1.541381265}
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