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marin [14]
3 years ago
6

Solve the equation by using the quadratic formula. 3 x squared minus 1 = 7 x

Mathematics
1 answer:
Paladinen [302]3 years ago
4 0

Answer:

b.  \frac{7+\sqrt{61} }{6} ,\frac{7-\sqrt{61} }{6}

Step-by-step explanation:

3x^{2} -1=7x

Quadratic equations are suppose to be written as: ax^2+bx+c=0

so the new quadratic equation for this problem will be: 3x^{2} -1-7x=0

Now rearrange the terms: 3x^{2} -7x-1=0

Then use the Quadratic Formula to Solve for the Quadratic Equation

Quadratic Formula = x=\frac{-b±}{} \frac{\sqrt{b^2-4ac} }{2a}

Note: Ignore the A in the quadratic formula

Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.

3x^{2} -7x-1=0

a = 3

b = -7

c = -1

x=-(-7)±\frac{\sqrt{(-7)^2-4(3)(-1)} }{2(3)}

Evaluate The Exponent

x=\frac{7±\sqrt{(49)-4(3)(-1)} }{2(3)}

Multiply The Numbers

x=\frac{7±\sqrt{49+12} }{2(3)}

Add The Numbers

x=\frac{7±\sqrt{61} }{2(3)}

Multiply The Numbers

x=\frac{7±\sqrt{61} }{6}

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