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Simplifying -3y(4y + 25) = 7y + -15 Reorder the terms: -3y(25 + 4y) = 7y + -15 (25 * -3y + 4y * -3y) = 7y + -15 (-75y + -12y2) = 7y + -15 Reorder the terms: -75y + -12y2 = -15 + 7y Solving -75y + -12y2 = -15 + 7y Solving for variable 'y'. Reorder the terms: 15 + -75y + -7y + -12y2 = -15 + 7y + 15 + -7y Combine like terms: -75y + -7y = -82y 15 + -82y + -12y2 = -15 + 7y + 15 + -7y Reorder the terms: 15 + -82y + -12y2 = -15 + 15 + 7y + -7y Combine like terms: -15 + 15 = 0 15 + -82y + -12y2 = 0 + 7y + -7y 15 + -82y + -12y2 = 7y + -7y Combine like terms: 7y + -7y = 0 15 + -82y + -12y2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -1.25 + 6.833333333y + y2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 6.833333333y + 1.25 + y2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 6.833333333y + y2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 6.833333333y + y2 = 0 + 1.25 6.833333333y + y2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 6.833333333y + y2 = 1.25 The y term is 6.833333333y. Take half its coefficient (3.416666667). Square it (11.67361111) and add it to both sides. Add '11.67361111' to each side of the equation. 6.833333333y + 11.67361111 + y2 = 1.25 + 11.67361111 Reorder the terms: 11.67361111 + 6.833333333y + y2 = 1.25 + 11.67361111 Combine like terms: 1.25 + 11.67361111 = 12.92361111 11.67361111 + 6.833333333y + y2 = 12.92361111 Factor a perfect square on the left side: (y + 3.416666667)(y + 3.416666667) = 12.92361111 Calculate the square root of the right side: 3.594942435 Break this problem into two subproblems by setting (y + 3.416666667) equal to 3.594942435 and -3.594942435.Subproblem 1
y + 3.416666667 = 3.594942435 Simplifying y + 3.416666667 = 3.594942435 Reorder the terms: 3.416666667 + y = 3.594942435 Solving 3.416666667 + y = 3.594942435 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.416666667' to each side of the equation. 3.416666667 + -3.416666667 + y = 3.594942435 + -3.416666667 Combine like terms: 3.416666667 + -3.416666667 = 0.000000000 0.000000000 + y = 3.594942435 + -3.416666667 y = 3.594942435 + -3.416666667 Combine like terms: 3.594942435 + -3.416666667 = 0.178275768 y = 0.178275768 Simplifying y = 0.178275768Subproblem 2
y + 3.416666667 = -3.594942435 Simplifying y + 3.416666667 = -3.594942435 Reorder the terms: 3.416666667 + y = -3.594942435 Solving 3.416666667 + y = -3.594942435 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.416666667' to each side of the equation. 3.416666667 + -3.416666667 + y = -3.594942435 + -3.416666667 Combine like terms: 3.416666667 + -3.416666667 = 0.000000000 0.000000000 + y = -3.594942435 + -3.416666667 y = -3.594942435 + -3.416666667 Combine like terms: -3.594942435 + -3.416666667 = -7.011609102 y = -7.011609102 Simplifying y = -7.011609102Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.178275768, -7.011609102}
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