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Simplifying 8y2 + -12y + -14 = y + 10 Reorder the terms: -14 + -12y + 8y2 = y + 10 Reorder the terms: -14 + -12y + 8y2 = 10 + y Solving -14 + -12y + 8y2 = 10 + y Solving for variable 'y'. Reorder the terms: -14 + -10 + -12y + -1y + 8y2 = 10 + y + -10 + -1y Combine like terms: -14 + -10 = -24 -24 + -12y + -1y + 8y2 = 10 + y + -10 + -1y Combine like terms: -12y + -1y = -13y -24 + -13y + 8y2 = 10 + y + -10 + -1y Reorder the terms: -24 + -13y + 8y2 = 10 + -10 + y + -1y Combine like terms: 10 + -10 = 0 -24 + -13y + 8y2 = 0 + y + -1y -24 + -13y + 8y2 = y + -1y Combine like terms: y + -1y = 0 -24 + -13y + 8y2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3 + -1.625y + y2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -1.625y + 3 + y2 = 0 + 3 Reorder the terms: -3 + 3 + -1.625y + y2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1.625y + y2 = 0 + 3 -1.625y + y2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1.625y + y2 = 3 The y term is -1.625y. Take half its coefficient (-0.8125). Square it (0.66015625) and add it to both sides. Add '0.66015625' to each side of the equation. -1.625y + 0.66015625 + y2 = 3 + 0.66015625 Reorder the terms: 0.66015625 + -1.625y + y2 = 3 + 0.66015625 Combine like terms: 3 + 0.66015625 = 3.66015625 0.66015625 + -1.625y + y2 = 3.66015625 Factor a perfect square on the left side: (y + -0.8125)(y + -0.8125) = 3.66015625 Calculate the square root of the right side: 1.913153483 Break this problem into two subproblems by setting (y + -0.8125) equal to 1.913153483 and -1.913153483.Subproblem 1
y + -0.8125 = 1.913153483 Simplifying y + -0.8125 = 1.913153483 Reorder the terms: -0.8125 + y = 1.913153483 Solving -0.8125 + y = 1.913153483 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.8125' to each side of the equation. -0.8125 + 0.8125 + y = 1.913153483 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + y = 1.913153483 + 0.8125 y = 1.913153483 + 0.8125 Combine like terms: 1.913153483 + 0.8125 = 2.725653483 y = 2.725653483 Simplifying y = 2.725653483Subproblem 2
y + -0.8125 = -1.913153483 Simplifying y + -0.8125 = -1.913153483 Reorder the terms: -0.8125 + y = -1.913153483 Solving -0.8125 + y = -1.913153483 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.8125' to each side of the equation. -0.8125 + 0.8125 + y = -1.913153483 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + y = -1.913153483 + 0.8125 y = -1.913153483 + 0.8125 Combine like terms: -1.913153483 + 0.8125 = -1.100653483 y = -1.100653483 Simplifying y = -1.100653483Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.725653483, -1.100653483}
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