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Simplifying (4y2 + 6y + -8) + -1(-9y + 4) = 0 Reorder the terms: (-8 + 6y + 4y2) + -1(-9y + 4) = 0 Remove parenthesis around (-8 + 6y + 4y2) -8 + 6y + 4y2 + -1(-9y + 4) = 0 Reorder the terms: -8 + 6y + 4y2 + -1(4 + -9y) = 0 -8 + 6y + 4y2 + (4 * -1 + -9y * -1) = 0 -8 + 6y + 4y2 + (-4 + 9y) = 0 Reorder the terms: -8 + -4 + 6y + 9y + 4y2 = 0 Combine like terms: -8 + -4 = -12 -12 + 6y + 9y + 4y2 = 0 Combine like terms: 6y + 9y = 15y -12 + 15y + 4y2 = 0 Solving -12 + 15y + 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'. -3 + 3.75y + y2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 3.75y + 3 + y2 = 0 + 3 Reorder the terms: -3 + 3 + 3.75y + y2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 3.75y + y2 = 0 + 3 3.75y + y2 = 0 + 3 Combine like terms: 0 + 3 = 3 3.75y + y2 = 3 The y term is 3.75y. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75y + 3.515625 + y2 = 3 + 3.515625 Reorder the terms: 3.515625 + 3.75y + y2 = 3 + 3.515625 Combine like terms: 3 + 3.515625 = 6.515625 3.515625 + 3.75y + y2 = 6.515625 Factor a perfect square on the left side: (y + 1.875)(y + 1.875) = 6.515625 Calculate the square root of the right side: 2.552572232 Break this problem into two subproblems by setting (y + 1.875) equal to 2.552572232 and -2.552572232.Subproblem 1
y + 1.875 = 2.552572232 Simplifying y + 1.875 = 2.552572232 Reorder the terms: 1.875 + y = 2.552572232 Solving 1.875 + y = 2.552572232 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + y = 2.552572232 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + y = 2.552572232 + -1.875 y = 2.552572232 + -1.875 Combine like terms: 2.552572232 + -1.875 = 0.677572232 y = 0.677572232 Simplifying y = 0.677572232Subproblem 2
y + 1.875 = -2.552572232 Simplifying y + 1.875 = -2.552572232 Reorder the terms: 1.875 + y = -2.552572232 Solving 1.875 + y = -2.552572232 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + y = -2.552572232 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + y = -2.552572232 + -1.875 y = -2.552572232 + -1.875 Combine like terms: -2.552572232 + -1.875 = -4.427572232 y = -4.427572232 Simplifying y = -4.427572232Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.677572232, -4.427572232}
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