To solve the quadratic equation [tex]\( 98 - x^2 = 0 \)[/tex], follow these steps:
1. Rewrite the Equation:
Start by rearranging the equation to isolate the quadratic term on one side:
[tex]\[ 98 - x^2 = 0 \][/tex]
This can be rewritten as:
[tex]\[ x^2 = 98 \][/tex]
2. Solve for [tex]\( x \)[/tex]:
To find [tex]\( x \)[/tex], take the square root of both sides of the equation:
[tex]\[ x = \pm \sqrt{98} \][/tex]
3. Simplify the Square Root:
Next, simplify [tex]\( \sqrt{98} \)[/tex]. Notice that:
[tex]\[ 98 = 2 \times 49 = 2 \times 7^2 \][/tex]
Therefore:
[tex]\[ \sqrt{98} = \sqrt{2 \times 7^2} = 7\sqrt{2} \][/tex]
4. Determine the Solutions:
Substitute back to find [tex]\( x \)[/tex]:
[tex]\[ x = \pm 7 \sqrt{2} \][/tex]
Thus, the solutions to the quadratic equation [tex]\( 98 - x^2 = 0 \)[/tex] are:
[tex]\[ x = \pm 7\sqrt{2} \][/tex]
Among the given options, the correct one is:
[tex]\[ x = \pm 7 \sqrt{2} \][/tex]
