Question

solve the following quadratic equation by completing square method x²+2x-8=0​

Answer 1

Answer:

here is the answer

Step-by-step explanation:

x²+2x-8=0

( 2-1 - 8 ) × ( x² + x ) = 0

7x³ =0

7x³ answer

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Answer 2

${x}^{2} + 2x - 8 = 0$

Completing the square :

$\\ {x}^{2} + 2x = 8 \\ \\ \implies \: adding \: 1 \: \: on \: \: both \: \: sides \\ \\ {x}^{2} + 2x + 1 = 8 + 1$

$\implies \: \: {x}^{2} + 2x + 1 \: \: is \: \: of \: \: the \: \: form \: \: {a}^{2} + 2ab+{b}^{2} \\ \: \: which \: \: can \: \: also \: \: be \: \: written \: \: as \: \: {(a + b)}^{2}$

$\implies \: here \: \: a = x \: \: and \: \: b = 1$

$\\ \\ {(x + 1)}^{2} = 9$

$\implies \: taking \: \: square \: \: to \: \: the \: \: otherside$

$\\ \\ x + 1 = \sqrt{9} \\ \\ x + 1 = ±3$

When x = +3 ;

$\\ x + 1 = 3 \\ \\ x = 3 - 1 \\ \\ \boxed{ x = 2}$

when x = (-3)

$\\ x + 1 = ( - 3) \\ \\ x = ( - 3) - 1 \\ \\ \boxed{ x = ( - 4)}$

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