Question

Which of the following represents the solutions x^2 -4x+12=6x-2

Answer 1

Given the equation:

`x^2-4x+12=6x-2`

Let's find the solution to the given equation.

Move all terms to the left and equate to zero.

Ad 2 and subtract 6x to both sides:

`\begin{gathered} x^2-4x-6x+12+2=6x-6x-2+2_{} \\ \\ x^2-10x+14=0 \end{gathered}`

Let's solve usingbthe quadratic formula:

`x=\frac{-b^{}\pm\sqrt[]{b^2-4ax}}{2a}`

Apply the general formula to find the values of a, b, and c:

`\begin{gathered} ax^2+bx+c=0 \\ \\ x^2-10x+14=0 \end{gathered}`

Thus, we have:

a = 1

b = -10

c = 14

Substitute the values into the quadratic formula:

`\begin{gathered} x=\frac{-(-10)\pm\sqrt[]{-10^2+4(1)(14)}}{2(1)} \\ \\ x=\frac{10\pm\sqrt[]{100+56_{}}}{2} \\ \\ x=\frac{10\pm\sqrt[]{44}}{2} \\ \\ x=\frac{10\pm\sqrt[]{4\ast11}}{2} \\ \\ x=\frac{10\pm\sqrt[]{2^2\ast11}}{2} \\ \\ x=\frac{10\pm2\sqrt[]{11}}{2} \\ \\ x=5\pm\sqrt[]{11} \end{gathered}`

Solving further:

`\begin{gathered} x=5+\sqrt[]{11},\text{ 5-}\sqrt[]{11} \\ \\ x=5+3.317,\text{ 5-3.31}7 \\ \\ x=8.317,\text{ 1.683} \end{gathered}`

Therefore, the solutions are:

x = 8.317, 1.683

ANSWER:

8.137 and 1.683