For this case we solve each of the equations:
[tex]2x ^ 2-32 = 0[/tex]
Adding 32 to both sides of the equation:
[tex]2x ^ 2 = 32[/tex]
Dividing between 2 on both sides of the equation:
[tex]x ^ 2 = \frac {32} {2}\\x ^ 2 = 16[/tex]
Applying square root to eliminate the exponent:
[tex]x = \pm \sqrt {16}\\x = \pm4\\x_ {1} = + 4\\x_ {2} = - 4[/tex]
Second equation:
[tex]4x ^ 2-100 = 0[/tex]
Adding 100 to both sides of the equation:
[tex]4x ^ 2 = 100[/tex]
Dividing between 4 on both sides of the equation:
[tex]x ^ 2 = \frac {100} {4}\\x ^ 2 = 25[/tex]
Applying square root to eliminate the exponent:
[tex]x = \pm \sqrt {25}\\x = \pm5\\x_ {1} = + 5\\x_ {2} = - 5[/tex]
Third equation:
[tex]x ^ 2-55 = 9[/tex]
Adding 55 to both sides of the equation:
[tex]x ^ 2 = 9 + 55\\x ^ 2 = 64[/tex]
Applying square root to eliminate the exponent:
[tex]x = \sqrt {64}\\x = \pm8[/tex]
Fourth equation:
[tex]x ^ 2-140 = -19[/tex]
Adding 140 to both sides of the equation:
[tex]x ^ 2 = -19 + 140\\x ^ 2 = 121[/tex]
Applying square root to eliminate the exponent:
[tex]x = \pm \sqrt {121}\\x = \pm11[/tex]
Fifth equation:
[tex]2x ^ 2-18 = 0[/tex]
Adding 18 to both sides of the equation:
2x ^ 2 = 18
Dividing between 2 on both sides of the equation:
[tex]x ^ 2 = \frac {18} {2}\\x ^ 2 = 9[/tex]
Applying square root to eliminate the exponent:
[tex]x = \pm \sqrt {9}\\x = \pm3[/tex]
Answer:
[tex]2x ^ 2-32 = 0, x_ {1} = + 4, x_ {2} = - 4\\4x ^ 2-100 = 0, x_ {1} = + 5, x_ {2} = - 5\\x ^ 2-55 = 9, x_ {1} = + 8, x_ {2} = - 8\\x ^ 2-140 = -19, x_ {1} = + 11, x_ {2} = - 11\\2x ^ 2-18 = 0, x_ {1} = + 3, x_ {2} = - 3[/tex]
