Problem of the Week

Updated at Jun 12, 2023 2:07 PM

How would you solve the equation 53−4x2=−597\frac{5}{3-4{x}^{2}}=-\frac{5}{97}?

Below is the solution.



53−4x2=−597\frac{5}{3-4{x}^{2}}=-\frac{5}{97}

1
Multiply both sides by 3−4x23-4{x}^{2}.
5=−597(3−4x2)5=-\frac{5}{97}(3-4{x}^{2})

2
Simplify  597(3−4x2)\frac{5}{97}(3-4{x}^{2})  to  5(3−4x2)97\frac{5(3-4{x}^{2})}{97}.
5=−5(3−4x2)975=-\frac{5(3-4{x}^{2})}{97}

3
Multiply both sides by 9797.
5×97=−5(3−4x2)5\times 97=-5(3-4{x}^{2})

4
Simplify  5×975\times 97  to  485485.
485=−5(3−4x2)485=-5(3-4{x}^{2})

5
Divide both sides by −5-5.
−4855=3−4x2-\frac{485}{5}=3-4{x}^{2}

6
Simplify  4855\frac{485}{5}  to  9797.
−97=3−4x2-97=3-4{x}^{2}

7
Subtract 33 from both sides.
−97−3=−4x2-97-3=-4{x}^{2}

8
Simplify  −97−3-97-3  to  −100-100.
−100=−4x2-100=-4{x}^{2}

9
Divide both sides by −4-4.
−100−4=x2\frac{-100}{-4}={x}^{2}

10
Two negatives make a positive.
1004=x2\frac{100}{4}={x}^{2}

11
Simplify  1004\frac{100}{4}  to  2525.
25=x225={x}^{2}

12
Take the square root of both sides.
±25=x\pm \sqrt{25}=x

13
Since 5×5=255\times 5=25, the square root of 2525 is 55.
±5=x\pm 5=x

14
Switch sides.
x=±5x=\pm 5

Done
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