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Simplifying 2y(5y + -2) = 15y + 6 Reorder the terms: 2y(-2 + 5y) = 15y + 6 (-2 * 2y + 5y * 2y) = 15y + 6 (-4y + 10y2) = 15y + 6 Reorder the terms: -4y + 10y2 = 6 + 15y Solving -4y + 10y2 = 6 + 15y Solving for variable 'y'. Reorder the terms: -6 + -4y + -15y + 10y2 = 6 + 15y + -6 + -15y Combine like terms: -4y + -15y = -19y -6 + -19y + 10y2 = 6 + 15y + -6 + -15y Reorder the terms: -6 + -19y + 10y2 = 6 + -6 + 15y + -15y Combine like terms: 6 + -6 = 0 -6 + -19y + 10y2 = 0 + 15y + -15y -6 + -19y + 10y2 = 15y + -15y Combine like terms: 15y + -15y = 0 -6 + -19y + 10y2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.6 + -1.9y + y2 = 0.0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -1.9y + 0.6 + y2 = 0.0 + 0.6 Reorder the terms: -0.6 + 0.6 + -1.9y + y2 = 0.0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -1.9y + y2 = 0.0 + 0.6 -1.9y + y2 = 0.0 + 0.6 Combine like terms: 0.0 + 0.6 = 0.6 -1.9y + y2 = 0.6 The y term is -1.9y. Take half its coefficient (-0.95). Square it (0.9025) and add it to both sides. Add '0.9025' to each side of the equation. -1.9y + 0.9025 + y2 = 0.6 + 0.9025 Reorder the terms: 0.9025 + -1.9y + y2 = 0.6 + 0.9025 Combine like terms: 0.6 + 0.9025 = 1.5025 0.9025 + -1.9y + y2 = 1.5025 Factor a perfect square on the left side: (y + -0.95)(y + -0.95) = 1.5025 Calculate the square root of the right side: 1.225765067 Break this problem into two subproblems by setting (y + -0.95) equal to 1.225765067 and -1.225765067.Subproblem 1
y + -0.95 = 1.225765067 Simplifying y + -0.95 = 1.225765067 Reorder the terms: -0.95 + y = 1.225765067 Solving -0.95 + y = 1.225765067 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.95' to each side of the equation. -0.95 + 0.95 + y = 1.225765067 + 0.95 Combine like terms: -0.95 + 0.95 = 0.00 0.00 + y = 1.225765067 + 0.95 y = 1.225765067 + 0.95 Combine like terms: 1.225765067 + 0.95 = 2.175765067 y = 2.175765067 Simplifying y = 2.175765067Subproblem 2
y + -0.95 = -1.225765067 Simplifying y + -0.95 = -1.225765067 Reorder the terms: -0.95 + y = -1.225765067 Solving -0.95 + y = -1.225765067 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.95' to each side of the equation. -0.95 + 0.95 + y = -1.225765067 + 0.95 Combine like terms: -0.95 + 0.95 = 0.00 0.00 + y = -1.225765067 + 0.95 y = -1.225765067 + 0.95 Combine like terms: -1.225765067 + 0.95 = -0.275765067 y = -0.275765067 Simplifying y = -0.275765067Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.175765067, -0.275765067}
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