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Simplifying (6y2 + -7y + -3) + (5y2 + -2y + 4) = 0 Reorder the terms: (-3 + -7y + 6y2) + (5y2 + -2y + 4) = 0 Remove parenthesis around (-3 + -7y + 6y2) -3 + -7y + 6y2 + (5y2 + -2y + 4) = 0 Reorder the terms: -3 + -7y + 6y2 + (4 + -2y + 5y2) = 0 Remove parenthesis around (4 + -2y + 5y2) -3 + -7y + 6y2 + 4 + -2y + 5y2 = 0 Reorder the terms: -3 + 4 + -7y + -2y + 6y2 + 5y2 = 0 Combine like terms: -3 + 4 = 1 1 + -7y + -2y + 6y2 + 5y2 = 0 Combine like terms: -7y + -2y = -9y 1 + -9y + 6y2 + 5y2 = 0 Combine like terms: 6y2 + 5y2 = 11y2 1 + -9y + 11y2 = 0 Solving 1 + -9y + 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 + -0.8181818182y + y2 = 0 Move the constant term to the right: Add '-0.09090909091' to each side of the equation. 0.09090909091 + -0.8181818182y + -0.09090909091 + y2 = 0 + -0.09090909091 Reorder the terms: 0.09090909091 + -0.09090909091 + -0.8181818182y + y2 = 0 + -0.09090909091 Combine like terms: 0.09090909091 + -0.09090909091 = 0.00000000000 0.00000000000 + -0.8181818182y + y2 = 0 + -0.09090909091 -0.8181818182y + y2 = 0 + -0.09090909091 Combine like terms: 0 + -0.09090909091 = -0.09090909091 -0.8181818182y + y2 = -0.09090909091 The y term is -0.8181818182y. Take half its coefficient (-0.4090909091). Square it (0.1673553719) and add it to both sides. Add '0.1673553719' to each side of the equation. -0.8181818182y + 0.1673553719 + y2 = -0.09090909091 + 0.1673553719 Reorder the terms: 0.1673553719 + -0.8181818182y + y2 = -0.09090909091 + 0.1673553719 Combine like terms: -0.09090909091 + 0.1673553719 = 0.07644628099 0.1673553719 + -0.8181818182y + y2 = 0.07644628099 Factor a perfect square on the left side: (y + -0.4090909091)(y + -0.4090909091) = 0.07644628099 Calculate the square root of the right side: 0.276489206 Break this problem into two subproblems by setting (y + -0.4090909091) equal to 0.276489206 and -0.276489206.Subproblem 1
y + -0.4090909091 = 0.276489206 Simplifying y + -0.4090909091 = 0.276489206 Reorder the terms: -0.4090909091 + y = 0.276489206 Solving -0.4090909091 + y = 0.276489206 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.4090909091' to each side of the equation. -0.4090909091 + 0.4090909091 + y = 0.276489206 + 0.4090909091 Combine like terms: -0.4090909091 + 0.4090909091 = 0.0000000000 0.0000000000 + y = 0.276489206 + 0.4090909091 y = 0.276489206 + 0.4090909091 Combine like terms: 0.276489206 + 0.4090909091 = 0.6855801151 y = 0.6855801151 Simplifying y = 0.6855801151Subproblem 2
y + -0.4090909091 = -0.276489206 Simplifying y + -0.4090909091 = -0.276489206 Reorder the terms: -0.4090909091 + y = -0.276489206 Solving -0.4090909091 + y = -0.276489206 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.4090909091' to each side of the equation. -0.4090909091 + 0.4090909091 + y = -0.276489206 + 0.4090909091 Combine like terms: -0.4090909091 + 0.4090909091 = 0.0000000000 0.0000000000 + y = -0.276489206 + 0.4090909091 y = -0.276489206 + 0.4090909091 Combine like terms: -0.276489206 + 0.4090909091 = 0.1326017031 y = 0.1326017031 Simplifying y = 0.1326017031Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.6855801151, 0.1326017031}
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