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Simplifying 0.6Q(Q) + 3.6Q + -7 = 0 Multiply Q * Q 0.6Q2 + 3.6Q + -7 = 0 Reorder the terms: -7 + 3.6Q + 0.6Q2 = 0 Solving -7 + 3.6Q + 0.6Q2 = 0 Solving for variable 'Q'. Begin completing the square. Divide all terms by 0.6 the coefficient of the squared term: Divide each side by '0.6'. -11.66666667 + 6Q + Q2 = 0 Move the constant term to the right: Add '11.66666667' to each side of the equation. -11.66666667 + 6Q + 11.66666667 + Q2 = 0 + 11.66666667 Reorder the terms: -11.66666667 + 11.66666667 + 6Q + Q2 = 0 + 11.66666667 Combine like terms: -11.66666667 + 11.66666667 = 0.00000000 0.00000000 + 6Q + Q2 = 0 + 11.66666667 6Q + Q2 = 0 + 11.66666667 Combine like terms: 0 + 11.66666667 = 11.66666667 6Q + Q2 = 11.66666667 The Q term is 6Q. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6Q + 9 + Q2 = 11.66666667 + 9 Reorder the terms: 9 + 6Q + Q2 = 11.66666667 + 9 Combine like terms: 11.66666667 + 9 = 20.66666667 9 + 6Q + Q2 = 20.66666667 Factor a perfect square on the left side: (Q + 3)(Q + 3) = 20.66666667 Calculate the square root of the right side: 4.546060566 Break this problem into two subproblems by setting (Q + 3) equal to 4.546060566 and -4.546060566.Subproblem 1
Q + 3 = 4.546060566 Simplifying Q + 3 = 4.546060566 Reorder the terms: 3 + Q = 4.546060566 Solving 3 + Q = 4.546060566 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + Q = 4.546060566 + -3 Combine like terms: 3 + -3 = 0 0 + Q = 4.546060566 + -3 Q = 4.546060566 + -3 Combine like terms: 4.546060566 + -3 = 1.546060566 Q = 1.546060566 Simplifying Q = 1.546060566Subproblem 2
Q + 3 = -4.546060566 Simplifying Q + 3 = -4.546060566 Reorder the terms: 3 + Q = -4.546060566 Solving 3 + Q = -4.546060566 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + Q = -4.546060566 + -3 Combine like terms: 3 + -3 = 0 0 + Q = -4.546060566 + -3 Q = -4.546060566 + -3 Combine like terms: -4.546060566 + -3 = -7.546060566 Q = -7.546060566 Simplifying Q = -7.546060566Solution
The solution to the problem is based on the solutions from the subproblems. Q = {1.546060566, -7.546060566}
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