Complete the square to solve 4x2 + 24x = 4?

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Complete the square to solve 4x2 + 24x = 4?

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Answer 1 · 2018-04-16T22:00:58

$x = 0.1623, - 6.1623$ $x=0.1623, -6.1623$

Explanation:

nothing can be in the $a$ $a$ spot to complete the square so divide everything by $4$ $4$
$x^{2} + 6 x = 1$ $x^2+6x=1$
Divide $b$ $b$ term by $2$ $2$ then square it:
${(\frac{6}{2})}^{2} = 9$ $(6/2)^2=9$
add to both sides:
$x^{2} + 6 x + 9 = 10$ $x^2+6x+9=10$
Now factor
Tip the factor is ALWAYS going to be the $b$ $b$ term divided by $2$ $2$ in this case that is $3$ $3$
${(x + 3)}^{2} = 10$ $(x+3)^2=10$
Square root both sides to get $x$ $x$ alone
$x + 3 = \pm \sqrt 10$ $x+3=+-√10$
$x = - 3 \pm \sqrt 10$ $x=-3+-√10$
$x = 0.1623, - 6.1623$ $x=0.1623, -6.1623$

Answer 2 · 2018-04-16T22:04:22

$x = - 3 \pm \sqrt{10}$ $x= -3+-sqrt(10)$

Explanation:

$4 x^{2} + 24 x = 4$ $4x^2+24x= 4$

Factor out the $4$ $4$
$4 (x^{2} + 6 x) = 4$ $4(x^2+6x)= 4$
Complete the square with ${(\frac{b}{2})}^{2}$ $(b/2)^2$ and add the same to the other side of the equal to sign:
$4 (x^{2} + 6 x + 9) = 4 + 36$ $4(x^2+6x+9)= 4+36$
Factor
$4 {(x + 3)}^{2} = 40$ $4(x+3)^2= 40$
Simplify
${(x + 3)}^{2} = 10$ $(x+3)^2= 10$

$x + 3 = \pm \sqrt{10}$ $x+3= +-sqrt(10)$

$x = - 3 \pm \sqrt{10}$ $x= -3+-sqrt(10)$

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Complete the square to solve 4x2 + 24x = 4?

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