Question

Express X^2 + 4X - 3 in the form (X+P)^2 + q

Answer 1

Answer:

Answer is (x + 2)² - 7

Step-by-step explanation:

• We gonna achieve this through completing squares:

${ \tt{ {x}^{2} + 4x - 3}}$

• Find the square of the half of the sum.

• sum is 4

${ \boxed{ \rm{square \: of \: sums \: half = {( \frac{4}{2} )}^{2} = {2}^{2} = 4 }}}$

• Add 4 to the sum and subtract it from the product.

• product is -3

$\hookrightarrow \: { \rm{ ({x}^{2} + 4x + 4) + ( - 3 - 4)}} \\ { \rm{(x + 2) {}^{2} - 7}}$

• Answer is proven

${ \boxed{ \mathfrak{answer \dashrightarrow \: { \rm{ {(x + 2)}^{2} - 7 }}}}}$

• P is 2
• q is -7