Question

Solve the equation x^2+4x-7=0 by completing the square

Answer 1

Answer:

given : x² + 4x - 7 = 0

to solve by completing the square

=> x² + 4x + 2² = 7 + 2²

[ take the coefficient of x, divide it by 2, square it and then add it to both sides of the equation ]

=> x² + 4x + 4 = 11

=> (x + 2)² = 11

=> x + 2 = ± √11

=> x = +√11 - 2 and x = -√11 - 2

Answer 2

Given,

An equation: x^2+4x-7=0

To find,

To solve the given equation by completing the square method.

Solution,

We can simply solve this mathematical problem using the following process:

According to the question;

x^2+4x-7=0

=> x^2+4x = 7

=> x^2+4x+4 = 7+4

=> x^2+4x+(2)^2 = 7+4

=> (x+2)^2 = 11

{Using the algebraic identity:

(a+b)^2 = a^2 + 2ab + b^2}

=> x+2 = +- √11

=> x = +- √11 - 2

=> x = (√11 - 2) and x = -√11 - 2 = -(√11+2)

Hence, both values of the given quadratic equation are (√11 - 2) and -(√11+2), respectively.