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Simplifying (-15y * -15y) + -10y = 1 Reorder the terms for easier multiplication: (-15 * -15y * y) + -10y = 1 Multiply -15 * -15 (225y * y) + -10y = 1 Multiply y * y (225y2) + -10y = 1 Reorder the terms: -10y + (225y2) = 1 Solving -10y + (225y2) = 1 Solving for variable 'y'. Reorder the terms: -1 + -10y + (225y2) = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -10y + (225y2) = 0 Begin completing the square. Divide all terms by 225 the coefficient of the squared term: Divide each side by '225'. -0.004444444444 + -0.04444444444y + y2 = 0 Move the constant term to the right: Add '0.004444444444' to each side of the equation. -0.004444444444 + -0.04444444444y + 0.004444444444 + y2 = 0 + 0.004444444444 Reorder the terms: -0.004444444444 + 0.004444444444 + -0.04444444444y + y2 = 0 + 0.004444444444 Combine like terms: -0.004444444444 + 0.004444444444 = 0.000000000000 0.000000000000 + -0.04444444444y + y2 = 0 + 0.004444444444 -0.04444444444y + y2 = 0 + 0.004444444444 Combine like terms: 0 + 0.004444444444 = 0.004444444444 -0.04444444444y + y2 = 0.004444444444 The y term is -0.04444444444y. Take half its coefficient (-0.02222222222). Square it (0.0004938271604) and add it to both sides. Add '0.0004938271604' to each side of the equation. -0.04444444444y + 0.0004938271604 + y2 = 0.004444444444 + 0.0004938271604 Reorder the terms: 0.0004938271604 + -0.04444444444y + y2 = 0.004444444444 + 0.0004938271604 Combine like terms: 0.004444444444 + 0.0004938271604 = 0.0049382716044 0.0004938271604 + -0.04444444444y + y2 = 0.0049382716044 Factor a perfect square on the left side: ((y) + -0.02222222222)((y) + -0.02222222222) = 0.0049382716044 Calculate the square root of the right side: 0.070272837 Break this problem into two subproblems by setting ((y) + -0.02222222222) equal to 0.070272837 and -0.070272837.Subproblem 1
(y) + -0.02222222222 = 0.070272837 Simplifying (y) + -0.02222222222 = 0.070272837 y + -0.02222222222 = 0.070272837 Reorder the terms: -0.02222222222 + y = 0.070272837 Solving -0.02222222222 + y = 0.070272837 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.02222222222' to each side of the equation. -0.02222222222 + 0.02222222222 + y = 0.070272837 + 0.02222222222 Combine like terms: -0.02222222222 + 0.02222222222 = 0.00000000000 0.00000000000 + y = 0.070272837 + 0.02222222222 y = 0.070272837 + 0.02222222222 Combine like terms: 0.070272837 + 0.02222222222 = 0.09249505922 y = 0.09249505922 Simplifying y = 0.09249505922Subproblem 2
(y) + -0.02222222222 = -0.070272837 Simplifying (y) + -0.02222222222 = -0.070272837 y + -0.02222222222 = -0.070272837 Reorder the terms: -0.02222222222 + y = -0.070272837 Solving -0.02222222222 + y = -0.070272837 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.02222222222' to each side of the equation. -0.02222222222 + 0.02222222222 + y = -0.070272837 + 0.02222222222 Combine like terms: -0.02222222222 + 0.02222222222 = 0.00000000000 0.00000000000 + y = -0.070272837 + 0.02222222222 y = -0.070272837 + 0.02222222222 Combine like terms: -0.070272837 + 0.02222222222 = -0.04805061478 y = -0.04805061478 Simplifying y = -0.04805061478Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.09249505922, -0.04805061478}
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