Answer:
1.√2x−1=5
Simplifies to:
1.414214x−1=5
Let's solve your equation step-by-step.
Step 1: Add 1 to both sides.
1.414214x−1+1=5+1
1.414214x=6
Step 2: Divide both sides by 1.414214.
1.414214x
1.414214
=
6
x=4.242639
2.Let's solve your equation step-by-step.
√x−4=0
Step 1: Add 4 to both sides.
√x−4+4=0+4
√x=4
Step 2: Solve Square Root.
x=42(Square both sides)
x=16
Check answers. (Plug them in to make sure they work.)
x=16(Works in original equation)
3.√3x−3=0
1.732051x−3=0
Step 1: Add 3 to both sides.
1.732051x−3+3=0+3
1.732051x=3
Step 2: Divide both sides by 1.732051.
1.732051x
1.732051
3
x=1.732051
4.√2x+1=2
1.414214x+1=2
Step 1: Subtract 1 from both sides.
1.414214x+1−1=2−1
1.414214x=1
1
x=0.707107
5.Let's solve your equation step-by-step.
√2x−3=√x
1.414214x−3=√x
Step 1: Flip the equation.
√x=1.414214x−3
x=(1.414214x−3)2(Square both sides)
x=2.000001x2−8.485284x+9
x−(2.000001x2−8.485284x+9)=2.000001x2−8.485284x+9−(2.000001x2−8.485284x+9)(Subtract 2.000001x^2-8.485284x+9 from both sides)
−2.000001x2+9.485284x−9=0
For this equation: a=-2.000001, b=9.485284, c=-9
−2.000001x2+9.485284x+−9=0
x=
−b±√b2−4ac
2a
(Use quadratic formula with a=-2.000001, b=9.485284, c=-9)
−(9.485284)±√(9.485284)2−4(−2.000001)(−9)
2(−2.000001)
−9.485284±√17.970577
−4.000002
x=1.3115274234064689,3.4311122052737164
x=1.311527(Doesn't work in original equation)
x=3.431112(Works in original equation)
x=3.431112
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Answers & Comments
Answer:
1.√2x−1=5
Simplifies to:
1.414214x−1=5
Let's solve your equation step-by-step.
1.414214x−1=5
Step 1: Add 1 to both sides.
1.414214x−1+1=5+1
1.414214x=6
Step 2: Divide both sides by 1.414214.
1.414214x
1.414214
=
6
1.414214
x=4.242639
Answer:
x=4.242639
2.Let's solve your equation step-by-step.
√x−4=0
Step 1: Add 4 to both sides.
√x−4+4=0+4
√x=4
Step 2: Solve Square Root.
√x=4
x=42(Square both sides)
x=16
Check answers. (Plug them in to make sure they work.)
x=16(Works in original equation)
Answer:
x=16
3.√3x−3=0
Simplifies to:
1.732051x−3=0
Let's solve your equation step-by-step.
1.732051x−3=0
Step 1: Add 3 to both sides.
1.732051x−3+3=0+3
1.732051x=3
Step 2: Divide both sides by 1.732051.
1.732051x
1.732051
=
3
1.732051
x=1.732051
Answer:
x=1.732051
4.√2x+1=2
Simplifies to:
1.414214x+1=2
Let's solve your equation step-by-step.
1.414214x+1=2
Step 1: Subtract 1 from both sides.
1.414214x+1−1=2−1
1.414214x=1
Step 2: Divide both sides by 1.414214.
1.414214x
1.414214
=
1
1.414214
x=0.707107
Answer:
x=0.707107
5.Let's solve your equation step-by-step.
√2x−3=√x
1.414214x−3=√x
Step 1: Flip the equation.
√x=1.414214x−3
Step 2: Solve Square Root.
√x=1.414214x−3
x=(1.414214x−3)2(Square both sides)
x=2.000001x2−8.485284x+9
x−(2.000001x2−8.485284x+9)=2.000001x2−8.485284x+9−(2.000001x2−8.485284x+9)(Subtract 2.000001x^2-8.485284x+9 from both sides)
−2.000001x2+9.485284x−9=0
For this equation: a=-2.000001, b=9.485284, c=-9
−2.000001x2+9.485284x+−9=0
x=
−b±√b2−4ac
2a
(Use quadratic formula with a=-2.000001, b=9.485284, c=-9)
x=
−(9.485284)±√(9.485284)2−4(−2.000001)(−9)
2(−2.000001)
x=
−9.485284±√17.970577
−4.000002
x=1.3115274234064689,3.4311122052737164
Check answers. (Plug them in to make sure they work.)
x=1.311527(Doesn't work in original equation)
x=3.431112(Works in original equation)
Answer:
x=3.431112