Question

2m² + 10 = 210
8b² - 7 = 193
how your
work!!!!!!!!!!!!!!!!!!!
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ow find the product of your
two solutions
answer =

Explanation:

Step1: Isolate the quadratic term for $m$

Subtract 10 from both sides:
$2m^2 = 210 - 10$
$2m^2 = 200$

Step2: Solve for $m^2$

Divide both sides by 2:
$m^2 = \frac{200}{2}$
$m^2 = 100$

Step3: Solve for $m$

Take square roots of both sides:
$m = \pm\sqrt{100}$
$m = 10 \text{ or } m = -10$

Step4: Isolate the quadratic term for $b$

Add 7 to both sides:
$8b^2 = 193 + 7$
$8b^2 = 200$

Step5: Solve for $b^2$

Divide both sides by 8:
$b^2 = \frac{200}{8}$
$b^2 = 25$

Step6: Solve for $b$

Take square roots of both sides:
$b = \pm\sqrt{25}$
$b = 5 \text{ or } b = -5$

Step7: Calculate product of all solutions

Multiply all four solutions:
$10 \times (-10) \times 5 \times (-5)$
First compute $10 \times (-10) = -100$, $5 \times (-5) = -25$
Then $-100 \times -25 = 2500$

Answer:

Solutions for $m$: $10, -10$
Solutions for $b$: $5, -5$
Product of all solutions: $2500$