Question

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$x ^{2} - x - 13 = 0$
solve this quadratic equation by completing the square​

Answer 1

$\huge{\boxed{\rm{\{\red{(1+√43)/2 and (1-√43)/2}}}}$

Explanation:

Given equation is x²-x-13=0

Solving this by completing the square method:-

=>x²-x=13

=>x²-(2/2)x=13

=>x²-2(x)(1/2)=13

on adding (1/2)² both sides then

=>x²-2(x)(1/2)+(1/2)²=13+(1/2)²

=>[x-(1/2)]²=13+(1/4)

=>[x-(1/2)]²=(42+1)/4

=>[x-(1/2)]²=43/4

=[x-(1/2)]=±√(43/4)

=>[x-(1/2)]=±√43/2

=>x=(1/2)±(√43/2)

=>x=(1/2)+(√43/2) or x=(1/2)-(√43/2)

=>X=(1+√43)/2 or x=(1-√43)/2

Roots are (1+√43)/2 and (1-√43)/2