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Simplifying 2y(5y + -1) = 15y + 3 Reorder the terms: 2y(-1 + 5y) = 15y + 3 (-1 * 2y + 5y * 2y) = 15y + 3 (-2y + 10y2) = 15y + 3 Reorder the terms: -2y + 10y2 = 3 + 15y Solving -2y + 10y2 = 3 + 15y Solving for variable 'y'. Reorder the terms: -3 + -2y + -15y + 10y2 = 3 + 15y + -3 + -15y Combine like terms: -2y + -15y = -17y -3 + -17y + 10y2 = 3 + 15y + -3 + -15y Reorder the terms: -3 + -17y + 10y2 = 3 + -3 + 15y + -15y Combine like terms: 3 + -3 = 0 -3 + -17y + 10y2 = 0 + 15y + -15y -3 + -17y + 10y2 = 15y + -15y Combine like terms: 15y + -15y = 0 -3 + -17y + 10y2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.3 + -1.7y + y2 = 0.0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + -1.7y + 0.3 + y2 = 0.0 + 0.3 Reorder the terms: -0.3 + 0.3 + -1.7y + y2 = 0.0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + -1.7y + y2 = 0.0 + 0.3 -1.7y + y2 = 0.0 + 0.3 Combine like terms: 0.0 + 0.3 = 0.3 -1.7y + y2 = 0.3 The y term is -1.7y. Take half its coefficient (-0.85). Square it (0.7225) and add it to both sides. Add '0.7225' to each side of the equation. -1.7y + 0.7225 + y2 = 0.3 + 0.7225 Reorder the terms: 0.7225 + -1.7y + y2 = 0.3 + 0.7225 Combine like terms: 0.3 + 0.7225 = 1.0225 0.7225 + -1.7y + y2 = 1.0225 Factor a perfect square on the left side: (y + -0.85)(y + -0.85) = 1.0225 Calculate the square root of the right side: 1.011187421 Break this problem into two subproblems by setting (y + -0.85) equal to 1.011187421 and -1.011187421.Subproblem 1
y + -0.85 = 1.011187421 Simplifying y + -0.85 = 1.011187421 Reorder the terms: -0.85 + y = 1.011187421 Solving -0.85 + y = 1.011187421 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.85' to each side of the equation. -0.85 + 0.85 + y = 1.011187421 + 0.85 Combine like terms: -0.85 + 0.85 = 0.00 0.00 + y = 1.011187421 + 0.85 y = 1.011187421 + 0.85 Combine like terms: 1.011187421 + 0.85 = 1.861187421 y = 1.861187421 Simplifying y = 1.861187421Subproblem 2
y + -0.85 = -1.011187421 Simplifying y + -0.85 = -1.011187421 Reorder the terms: -0.85 + y = -1.011187421 Solving -0.85 + y = -1.011187421 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.85' to each side of the equation. -0.85 + 0.85 + y = -1.011187421 + 0.85 Combine like terms: -0.85 + 0.85 = 0.00 0.00 + y = -1.011187421 + 0.85 y = -1.011187421 + 0.85 Combine like terms: -1.011187421 + 0.85 = -0.161187421 y = -0.161187421 Simplifying y = -0.161187421Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.861187421, -0.161187421}
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