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Simplifying 2y2 + -8y + y + -12y2 + -8y + 7 = 0 Reorder the terms: 7 + -8y + y + -8y + 2y2 + -12y2 = 0 Combine like terms: -8y + y = -7y 7 + -7y + -8y + 2y2 + -12y2 = 0 Combine like terms: -7y + -8y = -15y 7 + -15y + 2y2 + -12y2 = 0 Combine like terms: 2y2 + -12y2 = -10y2 7 + -15y + -10y2 = 0 Solving 7 + -15y + -10y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.7 + 1.5y + y2 = 0.0 Move the constant term to the right: Add '0.7' to each side of the equation. -0.7 + 1.5y + 0.7 + y2 = 0.0 + 0.7 Reorder the terms: -0.7 + 0.7 + 1.5y + y2 = 0.0 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + 1.5y + y2 = 0.0 + 0.7 1.5y + y2 = 0.0 + 0.7 Combine like terms: 0.0 + 0.7 = 0.7 1.5y + y2 = 0.7 The y term is 1.5y. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5y + 0.5625 + y2 = 0.7 + 0.5625 Reorder the terms: 0.5625 + 1.5y + y2 = 0.7 + 0.5625 Combine like terms: 0.7 + 0.5625 = 1.2625 0.5625 + 1.5y + y2 = 1.2625 Factor a perfect square on the left side: (y + 0.75)(y + 0.75) = 1.2625 Calculate the square root of the right side: 1.123610253 Break this problem into two subproblems by setting (y + 0.75) equal to 1.123610253 and -1.123610253.Subproblem 1
y + 0.75 = 1.123610253 Simplifying y + 0.75 = 1.123610253 Reorder the terms: 0.75 + y = 1.123610253 Solving 0.75 + y = 1.123610253 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + y = 1.123610253 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + y = 1.123610253 + -0.75 y = 1.123610253 + -0.75 Combine like terms: 1.123610253 + -0.75 = 0.373610253 y = 0.373610253 Simplifying y = 0.373610253Subproblem 2
y + 0.75 = -1.123610253 Simplifying y + 0.75 = -1.123610253 Reorder the terms: 0.75 + y = -1.123610253 Solving 0.75 + y = -1.123610253 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + y = -1.123610253 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + y = -1.123610253 + -0.75 y = -1.123610253 + -0.75 Combine like terms: -1.123610253 + -0.75 = -1.873610253 y = -1.873610253 Simplifying y = -1.873610253Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.373610253, -1.873610253}
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