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Simplifying 7y2 + -13y + -12 = 0 Reorder the terms: -12 + -13y + 7y2 = 0 Solving -12 + -13y + 7y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.714285714 + -1.857142857y + y2 = 0 Move the constant term to the right: Add '1.714285714' to each side of the equation. -1.714285714 + -1.857142857y + 1.714285714 + y2 = 0 + 1.714285714 Reorder the terms: -1.714285714 + 1.714285714 + -1.857142857y + y2 = 0 + 1.714285714 Combine like terms: -1.714285714 + 1.714285714 = 0.000000000 0.000000000 + -1.857142857y + y2 = 0 + 1.714285714 -1.857142857y + y2 = 0 + 1.714285714 Combine like terms: 0 + 1.714285714 = 1.714285714 -1.857142857y + y2 = 1.714285714 The y term is -1.857142857y. Take half its coefficient (-0.9285714285). Square it (0.8622448978) and add it to both sides. Add '0.8622448978' to each side of the equation. -1.857142857y + 0.8622448978 + y2 = 1.714285714 + 0.8622448978 Reorder the terms: 0.8622448978 + -1.857142857y + y2 = 1.714285714 + 0.8622448978 Combine like terms: 1.714285714 + 0.8622448978 = 2.5765306118 0.8622448978 + -1.857142857y + y2 = 2.5765306118 Factor a perfect square on the left side: (y + -0.9285714285)(y + -0.9285714285) = 2.5765306118 Calculate the square root of the right side: 1.605157504 Break this problem into two subproblems by setting (y + -0.9285714285) equal to 1.605157504 and -1.605157504.Subproblem 1
y + -0.9285714285 = 1.605157504 Simplifying y + -0.9285714285 = 1.605157504 Reorder the terms: -0.9285714285 + y = 1.605157504 Solving -0.9285714285 + y = 1.605157504 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.9285714285' to each side of the equation. -0.9285714285 + 0.9285714285 + y = 1.605157504 + 0.9285714285 Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000 0.0000000000 + y = 1.605157504 + 0.9285714285 y = 1.605157504 + 0.9285714285 Combine like terms: 1.605157504 + 0.9285714285 = 2.5337289325 y = 2.5337289325 Simplifying y = 2.5337289325Subproblem 2
y + -0.9285714285 = -1.605157504 Simplifying y + -0.9285714285 = -1.605157504 Reorder the terms: -0.9285714285 + y = -1.605157504 Solving -0.9285714285 + y = -1.605157504 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.9285714285' to each side of the equation. -0.9285714285 + 0.9285714285 + y = -1.605157504 + 0.9285714285 Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000 0.0000000000 + y = -1.605157504 + 0.9285714285 y = -1.605157504 + 0.9285714285 Combine like terms: -1.605157504 + 0.9285714285 = -0.6765860755 y = -0.6765860755 Simplifying y = -0.6765860755Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.5337289325, -0.6765860755}
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