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Dmitrij [34]
3 years ago
10

Solve using the quadratic formula: 3x=2x^2-2

Mathematics
1 answer:
Tomtit [17]3 years ago
7 0

Answer:

x=2\\x=-\frac{1}{2}

Step-by-step explanation:

1) Move terms to the left side.

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

2) Distribute.

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

3) Rearrange terms.

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

4) Common factor.

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

5) Divide both sides of the equation by the same term.

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

6) Use the quadratic formula.

x=\frac{-b+\sqrt{b^{2}-4ac } }{2a}

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

2x^{2} -3x-2=0\\a=2\\b=-3\\c=-2

x=\frac{-(-3)+\sqrt{(-3)^{2} -4*2(-2)} }{2*2}

7) Simplify.

Evaluate the exponent

x=\frac{3+\sqrt{(-3)^{2}-4*2(-2) } }{2*2}

x=\frac{3+\sqrt{9-4*2(-2)} }{2*2}

Multiply the numbers

x=\frac{3+\sqrt{9-4*2(-2)} }{2*2}

x=\frac{3+\sqrt{9+16} }{2*2}

Add the numbers

x=\frac{3+\sqrt{9+16} }{2*2}

x=\frac{3+\sqrt{25} }{2*2}

Evaluate the square root

x=\frac{3+\sqrt{25} }{2*2} \\x=\frac{3+5}{2*2}

Multiply the numbers

x=\frac{3+5}{2*2}

x=\frac{3+5}{4}

8) Seperate the equations.

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.

x=\frac{3+5}{4}

x=\frac{3-5}{4}

9) Solve.

Rearrange and isolate the variable to find each solution.

x=2\\x=-\frac{1}{2}

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<u>Step :-(a)</u>

               Given equation 34 - 5x = -21

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