Question

Determine the missing step for solving the quadratic equation by completing the square.

Answer 1

Answer:

Missing step is "Add and subtract 4 in the parenthesis." The resulted equation is $5=-6(x-2)^2+24$.

Step-by-step explanation:

The given equation is

$0=-6x^2+24x-5$

Step 1: Add 5 on both sides.

$5=-6x^2+24x$

Step 2: Taking out 6 as common factor.

$5=-6(x^2-4x)$

If an expression is defined as $x^2+bx$, then add $(\frac{b}{2})^2$ in the expression to make it perfect square.

Here b=-4,

$(\frac{b}{2})^2=(\frac{-4}{2})^2=4$

Step 3: Add and subtract 4 in the parenthesis.

$5=-6(x^2-4x+4-4)$

$5=-6(x62-4x+4)-6(-4)$

$5=-6(x-2)^2+24$                $[\becasue (a-b)^2=a^2-2ab+b^2]$

Step 4: Subtract 24 from both sides.

$5-24=-6(x-2)^2+24-24$

$-19=-6(x-2)^2$

Step 5: Divide both sides by -6.

$\frac{19}{6}=(x-2)^2$

Step 6: Taking square root on both sides.

$\pm \sqrt{\frac{19}{6}}=(x-2)$

Step 7: Add 2 on both sides.

$2\pm \sqrt{\frac{19}{6}}=x$

Therefore, the two solutions are $x=2\pm \sqrt{\frac{19}{6}}$.

Answer 2

Answer with Step-by-step explanation:

We are given that an equation

$-6x^2+24x-5=0$

We have to find the missing step for solving the quadratic equation by completing square.

$-6x^2+24x-5=0$

$-6(x^2-4x)=5$

$-6(x^2-2\times x\times 2+4)+24=5$

$-6(x-2)^2=5-24$

$-6(x-2)^2=-19$

$(x-2)^2=\frac{-19}{-6}$

$(x-2)^2=\frac{19}{6}$

$x-2=\pm\sqrt{\frac{19}{2}}$

$x=\pm\frac{19}{6}}+2$