Question

quadratic equation
completing square
x^2-11x-7=0
step-by-step

Answer 1

Given :

A quadratic equation $x^{2} -11x-7$.

To find :

The zeroes of the quadratic equation.

Step-by-step explanation:

• We can complete the square by following these steps.
• Formula we're going to use this.

       $-b$ ± $\frac{\sqrt{b^{2} -4ac}}{2a}$

• a is the co efficient of $x^{2}$, b is the co efficient of $x$, c is the constant.

      $a = 1,b=-11,c=-7$

• Substitute these values in the equation.

       $-(-11)$ ± $\frac{\sqrt{(11)^{2}-4(1)(-7) }}{2(1)}$

• Remove the brackets.

       $11$ ± $\sqrt{\frac{121+28}{2}}$

• Sum the values

       $11$ ± $\sqrt{\frac{149}{2}}$

• Divide the values.

       $11$ ± $\sqrt{74.5}$

• Root $\sqrt{74.5}$ is 8.6
• There are two values because of ±
• The two values will be

       $11+8.6,11-8.6$

• Sum and subtract the values.

       $19.6,2.4$

Final answer :

The zeroes of the quadratic equation are $19.6,2.4$