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son4ous [18]
3 years ago
14

Solve each quadratic equation. Show your work. 14. (2x – 1)(x + 7) = 0 15. x2 + 3x = 10 16. 4x2 = 100

Mathematics
1 answer:
andreyandreev [35.5K]3 years ago
6 0
14.  (2x - 1)(x + 7) = 0

Using the zero factor property, we know that either the first or second terms (or both) must be equal to 0 if their product is 0.  We can set each term equal to 0 to find the solutions:

2x - 1 = 0
2x = 1
x = 1/2

x + 7 = 0
x = -7

15.  x^{2} +3x=10

To solve this equation, you first need to set it equal to 0:

x^{2} +3x=10 \\ x^{2} +3x-10 = 0

Next, it can be factored:

x^{2} +3x-10 = 0 \\ (x+5)(x-2)=0

Finally, we can solve just like we did above:

x + 5 = 0
x = -5

x - 2 = 0
x = 2

16.  4x^2=100

First, you can simplify by dividing each side by 4:

4x^2=100 \\ x^2=25

Now, set the equation equal to 0:

x^2=25 \\ x^2-25=0

Next, factor:

x^2-25=0 \\ (x+5)(x-5)=0

Finally, find the solutions:

x + 5 = 0
x = -5

x - 5 = 0
x = 5
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