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Simplifying (4y2 + 9y + -7) + -1(-5y + 5) = 0 Reorder the terms: (-7 + 9y + 4y2) + -1(-5y + 5) = 0 Remove parenthesis around (-7 + 9y + 4y2) -7 + 9y + 4y2 + -1(-5y + 5) = 0 Reorder the terms: -7 + 9y + 4y2 + -1(5 + -5y) = 0 -7 + 9y + 4y2 + (5 * -1 + -5y * -1) = 0 -7 + 9y + 4y2 + (-5 + 5y) = 0 Reorder the terms: -7 + -5 + 9y + 5y + 4y2 = 0 Combine like terms: -7 + -5 = -12 -12 + 9y + 5y + 4y2 = 0 Combine like terms: 9y + 5y = 14y -12 + 14y + 4y2 = 0 Solving -12 + 14y + 4y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 7y + 2y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 7y + 2y2)' equal to zero and attempt to solve: Simplifying -6 + 7y + 2y2 = 0 Solving -6 + 7y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3 + 3.5y + y2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 3.5y + 3 + y2 = 0 + 3 Reorder the terms: -3 + 3 + 3.5y + y2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 3.5y + y2 = 0 + 3 3.5y + y2 = 0 + 3 Combine like terms: 0 + 3 = 3 3.5y + y2 = 3 The y term is 3.5y. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5y + 3.0625 + y2 = 3 + 3.0625 Reorder the terms: 3.0625 + 3.5y + y2 = 3 + 3.0625 Combine like terms: 3 + 3.0625 = 6.0625 3.0625 + 3.5y + y2 = 6.0625 Factor a perfect square on the left side: (y + 1.75)(y + 1.75) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (y + 1.75) equal to 2.46221445 and -2.46221445.Subproblem 1
y + 1.75 = 2.46221445 Simplifying y + 1.75 = 2.46221445 Reorder the terms: 1.75 + y = 2.46221445 Solving 1.75 + y = 2.46221445 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + y = 2.46221445 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + y = 2.46221445 + -1.75 y = 2.46221445 + -1.75 Combine like terms: 2.46221445 + -1.75 = 0.71221445 y = 0.71221445 Simplifying y = 0.71221445Subproblem 2
y + 1.75 = -2.46221445 Simplifying y + 1.75 = -2.46221445 Reorder the terms: 1.75 + y = -2.46221445 Solving 1.75 + y = -2.46221445 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + y = -2.46221445 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + y = -2.46221445 + -1.75 y = -2.46221445 + -1.75 Combine like terms: -2.46221445 + -1.75 = -4.21221445 y = -4.21221445 Simplifying y = -4.21221445Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.71221445, -4.21221445}Solution
y = {0.71221445, -4.21221445}
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