How do you solve $4 x^{2} + 8 x + 3 = 0$ $4x^2+8x+3=0$ by completing the square?

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How do you solve $4 x^{2} + 8 x + 3 = 0$ $4x^2+8x+3=0$ by completing the square?

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Answer 1 · 2017-05-24T00:29:41

$x = - \frac{1}{2} and x = - \frac{3}{2}$ $x = - 1/2 and x = - 3/2$

Explanation:

$4 x^{2} + 8 x + 3 = 0$ $4x^2 + 8x + 3 = 0$
$4 x^{2} + 8 x + 4 = - 3 + 4$ $4x^2 + 8x + 4 = - 3 + 4$
$4 (x^{2} + 2 x + 1) = 1$ $4(x^2 + 2x + 1) = 1$
${(x + 1)}^{2} = \frac{1}{4}$ $(x + 1)^2 = 1/4$
$x + 1 = \pm \frac{1}{2}$ $x + 1 = +- 1/2$
$x = - 1 \pm \frac{1}{2}$ $x = - 1 +- 1/2$
$x 1 = - \frac{1}{2}$ $x1 = - 1/2$
$x 2 = - \frac{3}{2}$ $x2 = - 3/2$

Answer 2 · 2017-05-24T00:42:02

Answer: $x = - \frac{1}{2}$ $x=-1/2$ and $x = - \frac{3}{2}$ $x=-3/2$

Explanation:

Step 1. Factor out any numbers in front of the $x^{2}$ $x^2$ term

$4 (x^{2} + 2 x + \frac{3}{4}) = 0$ $4(x^2+2x+3/4)=0$

Step 2. Cut the term in front of $x$ $x$ in half, then square it. Add and subtract the result inside the parenthesis

Term in front of $x$ $x$ : 2
Cut it in half: $1$ $1$
Square it: $1^{2} = 1$ $1^2=1$
Add and subtract that inside the parenthesis

$4 (x^{2} + 2 x + 1 - 1 + \frac{3}{4}) = 0$ $4(x^2+2x+1-1+3/4)=0$

Step 3. Isolate and rewrite your perfect square

Isolate the perfect square
$4 ((x^{2} + 2 x + 1) - 1 + \frac{3}{4}) = 0$ $4((x^2+2x+1)-1+3/4)=0$
Rewrite the perfect square
$4 ({(x + 1)}^{2} - 1 + \frac{3}{4}) = 0$ $4((x+1)^2-1+3/4)=0$
Simplify the remaining addition / subtraction term
$4 ({(x + 1)}^{2} - \frac{1}{4}) = 0$ $4((x+1)^2-1/4)=0$

Step 4. Multiply the coefficient term back through
$4 {(x + 1)}^{2} - 1 = 0$ $4(x+1)^2-1=0$

Step 5. Solve the equation

Add $1$ $1$ to both sides
$4 {(x + 1)}^{2} = 1$ $4(x+1)^2=1$
Divide both sides by $4$ $4$
${(x + 1)}^{2} = \frac{1}{4}$ $(x+1)^2=1/4$
Square root both sides
$x + 1 = \pm \sqrt{\frac{1}{4}}$ $x+1=+-sqrt(1/4)$
Subtract $1$ $1$ from both sides
$x = - 1 \pm \frac{1}{2}$ $x=-1+-1/2$

Answer: $x = - \frac{1}{2}$ $x=-1/2$ and $x = - \frac{3}{2}$ $x=-3/2$

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How do you solve $4 x^{2} + 8 x + 3 = 0$ $4x^2+8x+3=0$ by completing the square?

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