ANSWER
x=1.1 or x=-9.1
EXPLANATION
[tex] {x}^{2} + 8x = 10[/tex]
Ad the square of half the coefficient of x to both sides:
[tex]{x}^{2} + 8x + {4}^{2} = 10 + {4}^{2} [/tex]
[tex]{x}^{2} + 8x + 16= 10 + 16[/tex]
The left hand side is now a perfect square.
[tex] {(x + 4)}^{2} = 26[/tex]
Take square root
[tex]x + 4= \pm \sqrt{26}[/tex]
[tex]x = - 4 \pm \sqrt{26}[/tex]
x=1.1 or x=-9.1
Using the quadratic formula, we need to rewrite the given equation to get;
[tex] {x}^{2} + 8x - 10 = 0[/tex]
where a=1, b=8 and c=-10
The solution is given by:
[tex]x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
We substitute the values into the formula to get;
[tex]x = \frac{ - 8\pm \: \sqrt{ {8}^{2} - 4(1)( - 10) } }{2(1)} [/tex]
[tex]x = \frac{ - 8\pm \: \sqrt{ 104 } }{2} [/tex]
[tex]x = \frac{ - 8\pm \: 2\sqrt{ 26 } }{2} [/tex]
[tex]x = - 4\pm \: \sqrt{ 26 } [/tex]
x=1.1 or x=-9.1
to the nearest tenth.
