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Simplifying (y2 + -1y + -7) + (3 + -2y + 3y2) = 0 Reorder the terms: (-7 + -1y + y2) + (3 + -2y + 3y2) = 0 Remove parenthesis around (-7 + -1y + y2) -7 + -1y + y2 + (3 + -2y + 3y2) = 0 Remove parenthesis around (3 + -2y + 3y2) -7 + -1y + y2 + 3 + -2y + 3y2 = 0 Reorder the terms: -7 + 3 + -1y + -2y + y2 + 3y2 = 0 Combine like terms: -7 + 3 = -4 -4 + -1y + -2y + y2 + 3y2 = 0 Combine like terms: -1y + -2y = -3y -4 + -3y + y2 + 3y2 = 0 Combine like terms: y2 + 3y2 = 4y2 -4 + -3y + 4y2 = 0 Solving -4 + -3y + 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 + -0.75y + y2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.75y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + -0.75y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.75y + y2 = 0 + 1 -0.75y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.75y + y2 = 1 The y term is -0.75y. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75y + 0.140625 + y2 = 1 + 0.140625 Reorder the terms: 0.140625 + -0.75y + y2 = 1 + 0.140625 Combine like terms: 1 + 0.140625 = 1.140625 0.140625 + -0.75y + y2 = 1.140625 Factor a perfect square on the left side: (y + -0.375)(y + -0.375) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (y + -0.375) equal to 1.068000468 and -1.068000468.Subproblem 1
y + -0.375 = 1.068000468 Simplifying y + -0.375 = 1.068000468 Reorder the terms: -0.375 + y = 1.068000468 Solving -0.375 + y = 1.068000468 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + y = 1.068000468 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + y = 1.068000468 + 0.375 y = 1.068000468 + 0.375 Combine like terms: 1.068000468 + 0.375 = 1.443000468 y = 1.443000468 Simplifying y = 1.443000468Subproblem 2
y + -0.375 = -1.068000468 Simplifying y + -0.375 = -1.068000468 Reorder the terms: -0.375 + y = -1.068000468 Solving -0.375 + y = -1.068000468 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + y = -1.068000468 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + y = -1.068000468 + 0.375 y = -1.068000468 + 0.375 Combine like terms: -1.068000468 + 0.375 = -0.693000468 y = -0.693000468 Simplifying y = -0.693000468Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.443000468, -0.693000468}
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