Answer:
x = -1 + [tex]\sqrt{\frac{7}{4} }[/tex], x = -1 - [tex]\sqrt{\frac{7}{4} }[/tex]
Step-by-step explanation:
4[tex]x^{2}[/tex] + 8x - 3 = 0
First, add 3 to both sides:
4[tex]x^{2}[/tex] + 8x = 3
Next, divide both sides by 4:
[tex]x^{2}[/tex] + 2x = [tex]\frac{3}{4}[/tex]
Now, add the correct number by dividing 2 by 2 and squaring it and add it to both sides:
[tex]x^{2}[/tex] + 2x + 1 = [tex]\frac{7}{4}[/tex]
Then, factor the left side:
[tex](x + 1)^{2}[/tex] = [tex]\frac{7}{4}[/tex]
Next, take the square root of both sides:
x + 1 = ± [tex]\sqrt{\frac{7}{4} }[/tex]
Solve for x:
x = -1 + [tex]\sqrt{\frac{7}{4} }[/tex], x = -1 - [tex]\sqrt{\frac{7}{4} }[/tex]
