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Simplifying 0 = (4.8y2) + y + -6 Reorder the terms: 0 = -6 + y + (4.8y2) Solving 0 = -6 + y + (4.8y2) Solving for variable 'y'. Combine like terms: 0 + 6 = 6 6 + -1y + (-4.8y2) = -6 + y + (4.8y2) + 6 + -1y + (-4.8y2) Reorder the terms: 6 + -1y + (-4.8y2) = -6 + 6 + y + -1y + (4.8y2) + (-4.8y2) Combine like terms: -6 + 6 = 0 6 + -1y + (-4.8y2) = 0 + y + -1y + (4.8y2) + (-4.8y2) 6 + -1y + (-4.8y2) = y + -1y + (4.8y2) + (-4.8y2) Combine like terms: y + -1y = 0 6 + -1y + (-4.8y2) = 0 + (4.8y2) + (-4.8y2) 6 + -1y + (-4.8y2) = (4.8y2) + (-4.8y2) Combine like terms: (4.8y2) + (-4.8y2) = 0.0 6 + -1y + (-4.8y2) = 0.0 Begin completing the square. Divide all terms by -4.8 the coefficient of the squared term: Divide each side by '-4.8'. -1.25 + 0.2083333333y + y2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 0.2083333333y + 1.25 + y2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 0.2083333333y + y2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 0.2083333333y + y2 = 0 + 1.25 0.2083333333y + y2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 0.2083333333y + y2 = 1.25 The y term is 0.2083333333y. Take half its coefficient (0.1041666667). Square it (0.01085069445) and add it to both sides. Add '0.01085069445' to each side of the equation. 0.2083333333y + 0.01085069445 + y2 = 1.25 + 0.01085069445 Reorder the terms: 0.01085069445 + 0.2083333333y + y2 = 1.25 + 0.01085069445 Combine like terms: 1.25 + 0.01085069445 = 1.26085069445 0.01085069445 + 0.2083333333y + y2 = 1.26085069445 Factor a perfect square on the left side: ((y) + 0.1041666667)((y) + 0.1041666667) = 1.26085069445 Calculate the square root of the right side: 1.122876082 Break this problem into two subproblems by setting ((y) + 0.1041666667) equal to 1.122876082 and -1.122876082.Subproblem 1
(y) + 0.1041666667 = 1.122876082 Simplifying (y) + 0.1041666667 = 1.122876082 y + 0.1041666667 = 1.122876082 Reorder the terms: 0.1041666667 + y = 1.122876082 Solving 0.1041666667 + y = 1.122876082 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.1041666667' to each side of the equation. 0.1041666667 + -0.1041666667 + y = 1.122876082 + -0.1041666667 Combine like terms: 0.1041666667 + -0.1041666667 = 0.0000000000 0.0000000000 + y = 1.122876082 + -0.1041666667 y = 1.122876082 + -0.1041666667 Combine like terms: 1.122876082 + -0.1041666667 = 1.0187094153 y = 1.0187094153 Simplifying y = 1.0187094153Subproblem 2
(y) + 0.1041666667 = -1.122876082 Simplifying (y) + 0.1041666667 = -1.122876082 y + 0.1041666667 = -1.122876082 Reorder the terms: 0.1041666667 + y = -1.122876082 Solving 0.1041666667 + y = -1.122876082 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.1041666667' to each side of the equation. 0.1041666667 + -0.1041666667 + y = -1.122876082 + -0.1041666667 Combine like terms: 0.1041666667 + -0.1041666667 = 0.0000000000 0.0000000000 + y = -1.122876082 + -0.1041666667 y = -1.122876082 + -0.1041666667 Combine like terms: -1.122876082 + -0.1041666667 = -1.2270427487 y = -1.2270427487 Simplifying y = -1.2270427487Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.0187094153, -1.2270427487}
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