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Simplifying -10y + 18 = -3(5y + -7) * 5y Reorder the terms: 18 + -10y = -3(5y + -7) * 5y Reorder the terms: 18 + -10y = -3(-7 + 5y) * 5y Reorder the terms for easier multiplication: 18 + -10y = -3 * 5y(-7 + 5y) Multiply -3 * 5 18 + -10y = -15y(-7 + 5y) 18 + -10y = (-7 * -15y + 5y * -15y) 18 + -10y = (105y + -75y2) Solving 18 + -10y = 105y + -75y2 Solving for variable 'y'. Combine like terms: -10y + -105y = -115y 18 + -115y + 75y2 = 105y + -75y2 + -105y + 75y2 Reorder the terms: 18 + -115y + 75y2 = 105y + -105y + -75y2 + 75y2 Combine like terms: 105y + -105y = 0 18 + -115y + 75y2 = 0 + -75y2 + 75y2 18 + -115y + 75y2 = -75y2 + 75y2 Combine like terms: -75y2 + 75y2 = 0 18 + -115y + 75y2 = 0 Begin completing the square. Divide all terms by 75 the coefficient of the squared term: Divide each side by '75'. 0.24 + -1.533333333y + y2 = 0 Move the constant term to the right: Add '-0.24' to each side of the equation. 0.24 + -1.533333333y + -0.24 + y2 = 0 + -0.24 Reorder the terms: 0.24 + -0.24 + -1.533333333y + y2 = 0 + -0.24 Combine like terms: 0.24 + -0.24 = 0.00 0.00 + -1.533333333y + y2 = 0 + -0.24 -1.533333333y + y2 = 0 + -0.24 Combine like terms: 0 + -0.24 = -0.24 -1.533333333y + y2 = -0.24 The y term is -1.533333333y. Take half its coefficient (-0.7666666665). Square it (0.5877777775) and add it to both sides. Add '0.5877777775' to each side of the equation. -1.533333333y + 0.5877777775 + y2 = -0.24 + 0.5877777775 Reorder the terms: 0.5877777775 + -1.533333333y + y2 = -0.24 + 0.5877777775 Combine like terms: -0.24 + 0.5877777775 = 0.3477777775 0.5877777775 + -1.533333333y + y2 = 0.3477777775 Factor a perfect square on the left side: (y + -0.7666666665)(y + -0.7666666665) = 0.3477777775 Calculate the square root of the right side: 0.589726867 Break this problem into two subproblems by setting (y + -0.7666666665) equal to 0.589726867 and -0.589726867.Subproblem 1
y + -0.7666666665 = 0.589726867 Simplifying y + -0.7666666665 = 0.589726867 Reorder the terms: -0.7666666665 + y = 0.589726867 Solving -0.7666666665 + y = 0.589726867 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.7666666665' to each side of the equation. -0.7666666665 + 0.7666666665 + y = 0.589726867 + 0.7666666665 Combine like terms: -0.7666666665 + 0.7666666665 = 0.0000000000 0.0000000000 + y = 0.589726867 + 0.7666666665 y = 0.589726867 + 0.7666666665 Combine like terms: 0.589726867 + 0.7666666665 = 1.3563935335 y = 1.3563935335 Simplifying y = 1.3563935335Subproblem 2
y + -0.7666666665 = -0.589726867 Simplifying y + -0.7666666665 = -0.589726867 Reorder the terms: -0.7666666665 + y = -0.589726867 Solving -0.7666666665 + y = -0.589726867 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.7666666665' to each side of the equation. -0.7666666665 + 0.7666666665 + y = -0.589726867 + 0.7666666665 Combine like terms: -0.7666666665 + 0.7666666665 = 0.0000000000 0.0000000000 + y = -0.589726867 + 0.7666666665 y = -0.589726867 + 0.7666666665 Combine like terms: -0.589726867 + 0.7666666665 = 0.1769397995 y = 0.1769397995 Simplifying y = 0.1769397995Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.3563935335, 0.1769397995}
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