Final answer:
To solve the equation -4q+7=-(n-3)q², we can start by distributing the negative sign to the terms inside the parentheses. Next, bring all the terms to one side of the equation. Then, use factoring, completing the square, or the quadratic formula to solve for q. The values of q for which the equation is true are q=2+√11 and q=2-√11.
Step-by-step explanation:
To solve the equation -4q+7=-(n-3)q², we can start by distributing the negative sign to the terms inside the parentheses. This gives us -4q+7=q²-3q. Next, bring all the terms to one side of the equation to get q²-7q+3q-7=0. Combining like terms, we have q²-4q-7=0.
Now, we can use factoring, completing the square, or the quadratic formula to solve for q. Let's use the quadratic formula: q=(-(-4)±√((-4)²-4(1)(-7)))/(2(1)).
Simplifying this, we get q=(4±√(16+28))/2=q=(4±√44)/2=q=(4±2√11)/2.
Finally, simplifying further we have q=2±√11. So, the values of q for which the equation is true are q=2+√11 and q=2-√11.