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Simplifying 63 + 7Q + -3Q2 = 0 Solving 63 + 7Q + -3Q2 = 0 Solving for variable 'Q'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -21 + -2.333333333Q + Q2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + -2.333333333Q + 21 + Q2 = 0 + 21 Reorder the terms: -21 + 21 + -2.333333333Q + Q2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -2.333333333Q + Q2 = 0 + 21 -2.333333333Q + Q2 = 0 + 21 Combine like terms: 0 + 21 = 21 -2.333333333Q + Q2 = 21 The Q term is -2.333333333Q. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333Q + 1.361111112 + Q2 = 21 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333Q + Q2 = 21 + 1.361111112 Combine like terms: 21 + 1.361111112 = 22.361111112 1.361111112 + -2.333333333Q + Q2 = 22.361111112 Factor a perfect square on the left side: (Q + -1.166666667)(Q + -1.166666667) = 22.361111112 Calculate the square root of the right side: 4.728753653 Break this problem into two subproblems by setting (Q + -1.166666667) equal to 4.728753653 and -4.728753653.Subproblem 1
Q + -1.166666667 = 4.728753653 Simplifying Q + -1.166666667 = 4.728753653 Reorder the terms: -1.166666667 + Q = 4.728753653 Solving -1.166666667 + Q = 4.728753653 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + Q = 4.728753653 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + Q = 4.728753653 + 1.166666667 Q = 4.728753653 + 1.166666667 Combine like terms: 4.728753653 + 1.166666667 = 5.89542032 Q = 5.89542032 Simplifying Q = 5.89542032Subproblem 2
Q + -1.166666667 = -4.728753653 Simplifying Q + -1.166666667 = -4.728753653 Reorder the terms: -1.166666667 + Q = -4.728753653 Solving -1.166666667 + Q = -4.728753653 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + Q = -4.728753653 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + Q = -4.728753653 + 1.166666667 Q = -4.728753653 + 1.166666667 Combine like terms: -4.728753653 + 1.166666667 = -3.562086986 Q = -3.562086986 Simplifying Q = -3.562086986Solution
The solution to the problem is based on the solutions from the subproblems. Q = {5.89542032, -3.562086986}
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