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Simplifying (7y2 + -5y + -2) + (4y2 + -3y + 1) = 0 Reorder the terms: (-2 + -5y + 7y2) + (4y2 + -3y + 1) = 0 Remove parenthesis around (-2 + -5y + 7y2) -2 + -5y + 7y2 + (4y2 + -3y + 1) = 0 Reorder the terms: -2 + -5y + 7y2 + (1 + -3y + 4y2) = 0 Remove parenthesis around (1 + -3y + 4y2) -2 + -5y + 7y2 + 1 + -3y + 4y2 = 0 Reorder the terms: -2 + 1 + -5y + -3y + 7y2 + 4y2 = 0 Combine like terms: -2 + 1 = -1 -1 + -5y + -3y + 7y2 + 4y2 = 0 Combine like terms: -5y + -3y = -8y -1 + -8y + 7y2 + 4y2 = 0 Combine like terms: 7y2 + 4y2 = 11y2 -1 + -8y + 11y2 = 0 Solving -1 + -8y + 11y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.09090909091 + -0.7272727273y + y2 = 0 Move the constant term to the right: Add '0.09090909091' to each side of the equation. -0.09090909091 + -0.7272727273y + 0.09090909091 + y2 = 0 + 0.09090909091 Reorder the terms: -0.09090909091 + 0.09090909091 + -0.7272727273y + y2 = 0 + 0.09090909091 Combine like terms: -0.09090909091 + 0.09090909091 = 0.00000000000 0.00000000000 + -0.7272727273y + y2 = 0 + 0.09090909091 -0.7272727273y + y2 = 0 + 0.09090909091 Combine like terms: 0 + 0.09090909091 = 0.09090909091 -0.7272727273y + y2 = 0.09090909091 The y term is -0.7272727273y. Take half its coefficient (-0.3636363637). Square it (0.1322314050) and add it to both sides. Add '0.1322314050' to each side of the equation. -0.7272727273y + 0.1322314050 + y2 = 0.09090909091 + 0.1322314050 Reorder the terms: 0.1322314050 + -0.7272727273y + y2 = 0.09090909091 + 0.1322314050 Combine like terms: 0.09090909091 + 0.1322314050 = 0.22314049591 0.1322314050 + -0.7272727273y + y2 = 0.22314049591 Factor a perfect square on the left side: (y + -0.3636363637)(y + -0.3636363637) = 0.22314049591 Calculate the square root of the right side: 0.472377493 Break this problem into two subproblems by setting (y + -0.3636363637) equal to 0.472377493 and -0.472377493.Subproblem 1
y + -0.3636363637 = 0.472377493 Simplifying y + -0.3636363637 = 0.472377493 Reorder the terms: -0.3636363637 + y = 0.472377493 Solving -0.3636363637 + y = 0.472377493 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.3636363637' to each side of the equation. -0.3636363637 + 0.3636363637 + y = 0.472377493 + 0.3636363637 Combine like terms: -0.3636363637 + 0.3636363637 = 0.0000000000 0.0000000000 + y = 0.472377493 + 0.3636363637 y = 0.472377493 + 0.3636363637 Combine like terms: 0.472377493 + 0.3636363637 = 0.8360138567 y = 0.8360138567 Simplifying y = 0.8360138567Subproblem 2
y + -0.3636363637 = -0.472377493 Simplifying y + -0.3636363637 = -0.472377493 Reorder the terms: -0.3636363637 + y = -0.472377493 Solving -0.3636363637 + y = -0.472377493 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.3636363637' to each side of the equation. -0.3636363637 + 0.3636363637 + y = -0.472377493 + 0.3636363637 Combine like terms: -0.3636363637 + 0.3636363637 = 0.0000000000 0.0000000000 + y = -0.472377493 + 0.3636363637 y = -0.472377493 + 0.3636363637 Combine like terms: -0.472377493 + 0.3636363637 = -0.1087411293 y = -0.1087411293 Simplifying y = -0.1087411293Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.8360138567, -0.1087411293}
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