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 .