Solve the subsequent quadratic equation, Mathematics

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Solve the subsequent quadratic equation:

Solve the subsequent quadratic equation through taking the square roots of both sides.

3x2 = 100 - x2

Solution:

Step 1. Using the addition axiom, add x2 to both sides of the equation.

3x2  + x2          = 100 - x2  + x2

4x2       = 100

Step 2. Using the division axiom, divide both sides of the equation through 4.

4x 2 /4 = 100/4

x2  = 25

Step 3. Take the square root of both sides of the equation.

 

x2         = 25

√x2       = √25

x          = ±5

Thus, the roots are x = +5 and x = -5.

Step 4. Check the roots.

3x2       = 100 - x2

3(±5)2  = 100 - (±5)2

3(25)    = 100 - 25

75        = 75

If a pure quadratic equation is written in common form, a general expression can be written for its roots.  The common form of a pure quadratic is the subsequent.

ax2 + c = 0                                                                 

Using the subtraction axiom and subtract c from both sides of the equation.

ax2 = -c

Using the division axiom and divide both sides of the equation by a.

x2  = - c/a

Now take the square roots of both sides of the equation.

256_Solve the subsequent quadratic equation.png                                                            

Therefore, the roots of a pure quadratic equation written in common form ax2 + c = 0 are 1884_Solve the subsequent quadratic equation1.png.


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