**Solve the subsequent quadratic equation:**

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

3x^{2} = 100 - x^{2}

**Solution:**

**Step 1. **Using the addition axiom, add x^{2} to both sides of the equation.

3x^{2} + x^{2} = 100 - x^{2} + x^{2}

4x^{2} = 100

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

4x ^{2} /4 = 100/4

x^{2 } = 25

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

x^{2} = 25

√x^{2} = √25

x = ±5

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

**Step 4.** Check the roots.

3x^{2} = 100 - x^{2}

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.

ax^{2} + c = 0

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

ax^{2} = -c

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

x^{2} = - c/a

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

Therefore, the roots of a pure quadratic equation written in common form ax^{2} + c = 0 are .