9.7.4 Practice Spotting Calculation Errors

Algebra 19.7.4 Practice Spotting Calculation Errors

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Here is someone's solution to the equation $3 x^{2} - 4 x = 20$ .

Step 1 - $3 x^{2} - 4 x = 20$

Step 2 - $a = 3$ , $b = - 4$ , $c = 20$

Step 3 - $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

Step 4 - $x = \frac{- 4 \pm \sqrt{(- 4)^{2} - (4) (3) (20)}}{2 (3)}$

Step 5 - $x = \frac{- 4 \pm \sqrt{- 16 - 240}}{6}$

Step 6 - $x = \frac{- 4 \pm \sqrt{- 256}}{6}$

No Solutions

Identify as many errors as you can and briefly explain each error.

Compare your answer:

$b$ is -4, so in Step 4, the value $- b$ should be -(-4), which is 4.
In Step 1, the equation should be rewritten as $a x^{2} + b x + c = 0$ , so the constant term $c$ is -20, not 20. So, in Step 4, the last part of the numerator should be $\sqrt{(- 4)^{2} - 4 (3) (- 20)}$ .
In Step 4, $(- 4)^{2}$ should be 16. Squaring a negative number gives a positive number.
If the earlier issues were fixed, then the values under the square root symbol would be $16 + 240$ or 256.

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