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Simplifying (-2y2 + -5y) + (6y2 + y + -7) = 0 Reorder the terms: (-5y + -2y2) + (6y2 + y + -7) = 0 Remove parenthesis around (-5y + -2y2) -5y + -2y2 + (6y2 + y + -7) = 0 Reorder the terms: -5y + -2y2 + (-7 + y + 6y2) = 0 Remove parenthesis around (-7 + y + 6y2) -5y + -2y2 + -7 + y + 6y2 = 0 Reorder the terms: -7 + -5y + y + -2y2 + 6y2 = 0 Combine like terms: -5y + y = -4y -7 + -4y + -2y2 + 6y2 = 0 Combine like terms: -2y2 + 6y2 = 4y2 -7 + -4y + 4y2 = 0 Solving -7 + -4y + 4y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + -1y + y2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -1y + 1.75 + y2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -1y + y2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -1y + y2 = 0 + 1.75 -1y + y2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -1y + y2 = 1.75 The y term is -1y. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1y + 0.25 + y2 = 1.75 + 0.25 Reorder the terms: 0.25 + -1y + y2 = 1.75 + 0.25 Combine like terms: 1.75 + 0.25 = 2 0.25 + -1y + y2 = 2 Factor a perfect square on the left side: (y + -0.5)(y + -0.5) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (y + -0.5) equal to 1.414213562 and -1.414213562.Subproblem 1
y + -0.5 = 1.414213562 Simplifying y + -0.5 = 1.414213562 Reorder the terms: -0.5 + y = 1.414213562 Solving -0.5 + y = 1.414213562 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = 1.414213562 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = 1.414213562 + 0.5 y = 1.414213562 + 0.5 Combine like terms: 1.414213562 + 0.5 = 1.914213562 y = 1.914213562 Simplifying y = 1.914213562Subproblem 2
y + -0.5 = -1.414213562 Simplifying y + -0.5 = -1.414213562 Reorder the terms: -0.5 + y = -1.414213562 Solving -0.5 + y = -1.414213562 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = -1.414213562 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = -1.414213562 + 0.5 y = -1.414213562 + 0.5 Combine like terms: -1.414213562 + 0.5 = -0.914213562 y = -0.914213562 Simplifying y = -0.914213562Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.914213562, -0.914213562}
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