Step-by-step explanation:
1
Distribute
2
(
+
3
)
=
8
{\color{#c92786}{2s(s+3)}}=8
2s(s+3)=8
2
2
+
6
=
8
{\color{#c92786}{2s^{2}+6s}}=8
2s2+6s=8
2
Move terms to the left side
2
2
+
6
=
8
2s^{2}+6s=8
2s2+6s=8
2
2
+
6
−
8
=
0
2s^{2}+6s-8=0
2s2+6s−8=0
3
Common factor
2
2
+
6
−
8
=
0
2s^{2}+6s-8=0
2s2+6s−8=0
2
(
2
+
3
−
4
)
=
0
2(s^{2}+3s-4)=0
2(s2+3s−4)=0
4
Divide both sides of the equation by the same term
2
(
2
+
3
−
4
)
=
0
2(s^{2}+3s-4)=0
2(s2+3s−4)=0
2
+
3
−
4
=
0
s^{2}+3s-4=0
s2+3s−4=0
5
Use the quadratic formula
=
−
±
2
−
4
√
2
s=\frac{-{\color{#e8710a}{b}} \pm \sqrt{{\color{#e8710a}{b}}^{2}-4{\color{#c92786}{a}}{\color{#129eaf}{c}}}}{2{\color{#c92786}{a}}}
s=2a−b±b2−4ac
Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.
2
+
3
−
4
=
0
s^{2}+3s-4=0
s2+3s−4=0
=
1
a={\color{#c92786}{1}}
a=1
=
3
b={\color{#e8710a}{3}}
b=3
=
−
4
c={\color{#129eaf}{-4}}
c=−4
=
−
3
±
3
2
−
4
⋅
1
(
−
4
)
√
2
⋅
1
s=\frac{-{\color{#e8710a}{3}} \pm \sqrt{{\color{#e8710a}{3}}^{2}-4 \cdot {\color{#c92786}{1}}({\color{#129eaf}{-4}})}}{2 \cdot {\color{#c92786}{1}}}
s=2⋅1−3±32−4⋅1(−4)
6
Simplify
Evaluate the exponent
Multiply the numbers
Add the numbers
Evaluate the square root
Multiply the numbers
=
−
3
±
5
2
s=\frac{-3 \pm 5}{2}
s=2−3±5
7
Separate the equations
To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.
=
−
3
+
5
2
s=\frac{-3+5}{2}
s=2−3+5
=
−
3
−
5
2
s=\frac{-3-5}{2}
s=2−3−5
8
Solve
Rearrange and isolate the variable to find each solution
=
1
s=1
s=1
=
−
4
