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Simplifying (5y2 + 9y + -1) + (6y2 + 5y + -7) + -1(-3y2 + -8y + 6) = 0 Reorder the terms: (-1 + 9y + 5y2) + (6y2 + 5y + -7) + -1(-3y2 + -8y + 6) = 0 Remove parenthesis around (-1 + 9y + 5y2) -1 + 9y + 5y2 + (6y2 + 5y + -7) + -1(-3y2 + -8y + 6) = 0 Reorder the terms: -1 + 9y + 5y2 + (-7 + 5y + 6y2) + -1(-3y2 + -8y + 6) = 0 Remove parenthesis around (-7 + 5y + 6y2) -1 + 9y + 5y2 + -7 + 5y + 6y2 + -1(-3y2 + -8y + 6) = 0 Reorder the terms: -1 + 9y + 5y2 + -7 + 5y + 6y2 + -1(6 + -8y + -3y2) = 0 -1 + 9y + 5y2 + -7 + 5y + 6y2 + (6 * -1 + -8y * -1 + -3y2 * -1) = 0 -1 + 9y + 5y2 + -7 + 5y + 6y2 + (-6 + 8y + 3y2) = 0 Reorder the terms: -1 + -7 + -6 + 9y + 5y + 8y + 5y2 + 6y2 + 3y2 = 0 Combine like terms: -1 + -7 = -8 -8 + -6 + 9y + 5y + 8y + 5y2 + 6y2 + 3y2 = 0 Combine like terms: -8 + -6 = -14 -14 + 9y + 5y + 8y + 5y2 + 6y2 + 3y2 = 0 Combine like terms: 9y + 5y = 14y -14 + 14y + 8y + 5y2 + 6y2 + 3y2 = 0 Combine like terms: 14y + 8y = 22y -14 + 22y + 5y2 + 6y2 + 3y2 = 0 Combine like terms: 5y2 + 6y2 = 11y2 -14 + 22y + 11y2 + 3y2 = 0 Combine like terms: 11y2 + 3y2 = 14y2 -14 + 22y + 14y2 = 0 Solving -14 + 22y + 14y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 11y + 7y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + 11y + 7y2)' equal to zero and attempt to solve: Simplifying -7 + 11y + 7y2 = 0 Solving -7 + 11y + 7y2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1 + 1.571428571y + y2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.571428571y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + 1.571428571y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.571428571y + y2 = 0 + 1 1.571428571y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.571428571y + y2 = 1 The y term is 1.571428571y. Take half its coefficient (0.7857142855). Square it (0.6173469384) and add it to both sides. Add '0.6173469384' to each side of the equation. 1.571428571y + 0.6173469384 + y2 = 1 + 0.6173469384 Reorder the terms: 0.6173469384 + 1.571428571y + y2 = 1 + 0.6173469384 Combine like terms: 1 + 0.6173469384 = 1.6173469384 0.6173469384 + 1.571428571y + y2 = 1.6173469384 Factor a perfect square on the left side: (y + 0.7857142855)(y + 0.7857142855) = 1.6173469384 Calculate the square root of the right side: 1.271749558 Break this problem into two subproblems by setting (y + 0.7857142855) equal to 1.271749558 and -1.271749558.Subproblem 1
y + 0.7857142855 = 1.271749558 Simplifying y + 0.7857142855 = 1.271749558 Reorder the terms: 0.7857142855 + y = 1.271749558 Solving 0.7857142855 + y = 1.271749558 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.7857142855' to each side of the equation. 0.7857142855 + -0.7857142855 + y = 1.271749558 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + y = 1.271749558 + -0.7857142855 y = 1.271749558 + -0.7857142855 Combine like terms: 1.271749558 + -0.7857142855 = 0.4860352725 y = 0.4860352725 Simplifying y = 0.4860352725Subproblem 2
y + 0.7857142855 = -1.271749558 Simplifying y + 0.7857142855 = -1.271749558 Reorder the terms: 0.7857142855 + y = -1.271749558 Solving 0.7857142855 + y = -1.271749558 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.7857142855' to each side of the equation. 0.7857142855 + -0.7857142855 + y = -1.271749558 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + y = -1.271749558 + -0.7857142855 y = -1.271749558 + -0.7857142855 Combine like terms: -1.271749558 + -0.7857142855 = -2.0574638435 y = -2.0574638435 Simplifying y = -2.0574638435Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.4860352725, -2.0574638435}Solution
y = {0.4860352725, -2.0574638435}
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