Question

1) Solve the following quadritic equations by completing the square: i) X ² + 12x + = 15t 2 (i) x ~ 14x + 36=0

Answer 1

EXPLANATION

Filling the equation give us the following expression:

x^2 -14x + 36 = 0

Applying the square root relationship:

`x_1,x_2=\frac{-b\pm\sqrt[]{b^2-4\cdot a\cdot c}}{2\cdot a}`

Where a=1, b=-14, c=36

Replacing terms:

`x_1,x_2=\frac{-(-14)\pm\sqrt[]{(14)^2-4\cdot1\cdot36}}{2\cdot1}`

Multiplying numbers:

`x_1,x_2=\frac{14\pm\sqrt[]{196-144}}{2}`

Subtracting numbers:

`x_1,x_2=\frac{14\pm\sqrt[]{52}}{2}`

Solving the square root:

`x_(1,)x_2=\frac{14\pm2\sqrt[]{13}}{2}`

The solutions are:

`x_1=\frac{14+2\sqrt[]{13}}{2}=7+\sqrt[]{13}`
`x_2=7-\sqrt[]{13}`