Question

Solve this quadratic equation by completing the square x^2=12x+17

Answer 1

Answer:

$\large\boxed{\red{\sf x =6+\sqrt{53},6-\sqrt{53}} }$

Step-by-step explanation:

We would like to solve the given quadratic equation by completing the square method .The given equation is ;

$\longrightarrow x^2=12x +17$

Subtract 12x to both sides ,

$\longrightarrow x^2-12x = 17$

Here the co-efficient of x² is already 1 . So , we shall rewrite it as ,

$\longrightarrow x^2-2(6)(x) = 17$

Add 6² on both sides ,

$\longrightarrow x^2-2(6)(x) + 6^2=17+6^2$

Now LHS is in the form of (a-b)² = a²-2ab+b² ; so that ;

$\longrightarrow (x -6)^2 = 17+36$

Simplify RHS ,

$\longrightarrow (x-6)^2=53$

Put square root on both sides,

$\longrightarrow (x-6) = \pm\sqrt{53}$

Add 6 on both sides,

$\longrightarrow x = 6\pm\sqrt{53}$

Separate the two solutions ,

$\longrightarrow \underline{\underline{x =6+\sqrt{53},6-\sqrt{53}}}$

And we are done!