Answer:
(a) 1
(b) 1
(c) 3.03
Step-by-step explanation:
The given quadratic equation is
[tex]4x^2+8x+27=88[/tex]
Subtract 27 from both sides.
[tex]4x^2+8x=88-27[/tex]
[tex]4x^2+8x=61[/tex]
Taking out common factor.
[tex]4(x^2+2x)=61[/tex]
Divide both sides by 4.
[tex]x^2+2x=\dfrac{61}{4}[/tex]
If an expression is [tex]x^2+bx[/tex], then we need to add [tex](\frac{b}{2})^2[/tex], to make it perfect square.
Here, b=2, so [tex](\frac{2}{2})^2=1[/tex]
Add 1 on both sides.
[tex]x^2+2x+1=\dfrac{61}{4}+1[/tex]
[tex](x+1)^2=\dfrac{65}{4}[/tex]
Taking square root on both sides.
[tex](x+1)=\pm \sqrt{\dfrac{65}{4}}[/tex]
Subtract 1 from both sides.
[tex]x=-1\pm \sqrt{\dfrac{65}{4}}[/tex]
[tex]x=-1\pm 4.03[/tex]
[tex]x=-1+4.031[/tex] and [tex]x=-1-4.031[/tex]
[tex]x=3.031[/tex] and [tex]x=-5.031[/tex]
Only one solution is positive.
Greatest solution is 3.031, therefore the approximate value of this solution is 3.03.
