express both side into square and solve
a) x^2+x+(1/2)^2=(1/2)^2+6
Answers
Answer:
Evaluate the exponent
2
+
+
(
1
2
)
2
=
(
1
2
)
2
+
6
x^{2}+x+{\color{#c92786}{\left(\frac{1}{2}\right)^{2}}}=(\frac{1}{2})^{2}+6
x2+x+(21)2=(21)2+6
2
+
+
1
4
=
(
1
2
)
2
+
6
x^{2}+x+{\color{#c92786}{\frac{1}{4}}}=(\frac{1}{2})^{2}+6
x2+x+41=(21)2+6
2
Evaluate the exponent
2
+
+
1
4
=
(
1
2
)
2
+
6
x^{2}+x+\frac{1}{4}={\color{#c92786}{\left(\frac{1}{2}\right)^{2}}}+6
x2+x+41=(21)2+6
2
+
+
1
4
=
1
4
+
6
x^{2}+x+\frac{1}{4}={\color{#c92786}{\frac{1}{4}}}+6
x2+x+41=41+6
3
Add the numbers
2
+
+
1
4
=
1
4
+
6
x^{2}+x+\frac{1}{4}={\color{#c92786}{\frac{1}{4}}}+{\color{#c92786}{6}}
x2+x+41=41+6
2
+
+
1
4
=
2
5
4
x^{2}+x+\frac{1}{4}={\color{#c92786}{\frac{25}{4}}}
x2+x+41=425
4
Move terms to the left side
2
+
+
1
4
=
2
5
4
x^{2}+x+\frac{1}{4}=\frac{25}{4}
x2+x+41=425
2
+
+
1
4
−
2
5
4
=
0
x^{2}+x+\frac{1}{4}-\frac{25}{4}=0
x2+x+41−425=0
5
Subtract the numbers
2
+
+
1
4
−
2
5
4
=
0
x^{2}+x+{\color{#c92786}{\frac{1}{4}}}{\color{#c92786}{-\frac{25}{4}}}=0
x2+x+41−425=0
2
+
−
6
=
0
x^{2}+x{\color{#c92786}{-6}}=0
x2+x−6=0
6
Use the quadratic formula
=
−
±
2
−
4
√
2
x=\frac{-{\color{#e8710a}{b}} \pm \sqrt{{\color{#e8710a}{b}}^{2}-4{\color{#c92786}{a}}{\color{#129eaf}{c}}}}{2{\color{#c92786}{a}}}
x=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
+
−
6
=
0
x^{2}+x-6=0
x2+x−6=0
=
1
a={\color{#c92786}{1}}
a=1
=
1
b={\color{#e8710a}{1}}
b=1
=
−
6
c={\color{#129eaf}{-6}}
c=−6
=
−
1
±
1
2
−
4
⋅
1
(
−
6
)
√
2
⋅
1
x=\frac{-{\color{#e8710a}{1}} \pm \sqrt{{\color{#e8710a}{1}}^{2}-4 \cdot {\color{#c92786}{1}}({\color{#129eaf}{-6}})}}{2 \cdot {\color{#c92786}{1}}}
x=2⋅1−1±12−4⋅1(−6)
7
Simplify
Evaluate the exponent
Multiply the numbers
Add the numbers
Evaluate the square root
Multiply the numbers
=
−
1
±
5
2
x=\frac{-1 \pm 5}{2}
x=2−1±5
8
Separate the equations
To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.
=
−
1
+
5
2
x=\frac{-1+5}{2}
x=2−1+5
=
−
1
−
5
2
x=\frac{-1-5}{2}
x=2−1−5
9
Solve
Rearrange and isolate the variable to find each solution
=
2
x=2
x=2
=
−
3
Step-by-step explanation:
DON'T KNOW
SOORY
PLEASE MARK ME AS BRAINLIST