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Simplifying (5y2 + -1y + 3) + (-7y2 + -4y + 6) = 0 Reorder the terms: (3 + -1y + 5y2) + (-7y2 + -4y + 6) = 0 Remove parenthesis around (3 + -1y + 5y2) 3 + -1y + 5y2 + (-7y2 + -4y + 6) = 0 Reorder the terms: 3 + -1y + 5y2 + (6 + -4y + -7y2) = 0 Remove parenthesis around (6 + -4y + -7y2) 3 + -1y + 5y2 + 6 + -4y + -7y2 = 0 Reorder the terms: 3 + 6 + -1y + -4y + 5y2 + -7y2 = 0 Combine like terms: 3 + 6 = 9 9 + -1y + -4y + 5y2 + -7y2 = 0 Combine like terms: -1y + -4y = -5y 9 + -5y + 5y2 + -7y2 = 0 Combine like terms: 5y2 + -7y2 = -2y2 9 + -5y + -2y2 = 0 Solving 9 + -5y + -2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -4.5 + 2.5y + y2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 2.5y + 4.5 + y2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 2.5y + y2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 2.5y + y2 = 0 + 4.5 2.5y + y2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 2.5y + y2 = 4.5 The y term is 2.5y. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5y + 1.5625 + y2 = 4.5 + 1.5625 Reorder the terms: 1.5625 + 2.5y + y2 = 4.5 + 1.5625 Combine like terms: 4.5 + 1.5625 = 6.0625 1.5625 + 2.5y + y2 = 6.0625 Factor a perfect square on the left side: (y + 1.25)(y + 1.25) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (y + 1.25) equal to 2.46221445 and -2.46221445.Subproblem 1
y + 1.25 = 2.46221445 Simplifying y + 1.25 = 2.46221445 Reorder the terms: 1.25 + y = 2.46221445 Solving 1.25 + y = 2.46221445 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + y = 2.46221445 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + y = 2.46221445 + -1.25 y = 2.46221445 + -1.25 Combine like terms: 2.46221445 + -1.25 = 1.21221445 y = 1.21221445 Simplifying y = 1.21221445Subproblem 2
y + 1.25 = -2.46221445 Simplifying y + 1.25 = -2.46221445 Reorder the terms: 1.25 + y = -2.46221445 Solving 1.25 + y = -2.46221445 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + y = -2.46221445 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + y = -2.46221445 + -1.25 y = -2.46221445 + -1.25 Combine like terms: -2.46221445 + -1.25 = -3.71221445 y = -3.71221445 Simplifying y = -3.71221445Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.21221445, -3.71221445}
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