x(2x-1)=17

Simplify by multiplying through.

Apply the distributive property.

x(2x)+x⋅-1=17

Reorder.

Rewrite using the commutative property of multiplication.

2x⋅x+x⋅-1=17

Move -1 to the left of x.

2x⋅x-1⋅x=17

2x⋅x-1⋅x=17

2x⋅x-1⋅x=17

Simplify each term.

Multiply x by x by adding the exponents.

Move x.

2(x⋅x)-1⋅x=17

Multiply x by x.

2×2-1⋅x=17

2×2-1⋅x=17

Rewrite -1x as -x.

2×2-x=17

2×2-x=17

2×2-x=17

Move 17 to the left side of the equation by subtracting it from both sides.

2×2-x-17=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=2, b=-1, and c=-17 into the quadratic formula and solve for x.

1±(-1)2-4⋅(2⋅-17)2⋅2

Simplify the numerator.

Raise -1 to the power of 2.

x=1±1-4⋅(2⋅-17)2⋅2

Multiply 2 by -17.

x=1±1-4⋅-342⋅2

Multiply -4 by -34.

x=1±1+1362⋅2

Add 1 and 136.

x=1±1372⋅2

x=1±1372⋅2

Multiply 2 by 2.

x=1±1374

x=1±1374

Simplify the numerator.

Raise -1 to the power of 2.

x=1±1-4⋅(2⋅-17)2⋅2

Multiply 2 by -17.

x=1±1-4⋅-342⋅2

Multiply -4 by -34.

x=1±1+1362⋅2

Add 1 and 136.

x=1±1372⋅2

x=1±1372⋅2

Multiply 2 by 2.

x=1±1374

Change the ± to +.

x=1+1374

x=1+1374

Simplify the numerator.

Raise -1 to the power of 2.

x=1±1-4⋅(2⋅-17)2⋅2

Multiply 2 by -17.

x=1±1-4⋅-342⋅2

Multiply -4 by -34.

x=1±1+1362⋅2

Add 1 and 136.

x=1±1372⋅2

x=1±1372⋅2

Multiply 2 by 2.

x=1±1374

Change the ± to -.

x=1-1374

x=1-1374

The final answer is the combination of both solutions.

x=1+1374,1-1374

The result can be shown in multiple forms.

Exact Form:

x=1+1374,1-1374

Decimal Form:

x=3.17617497…,-2.67617497…

Solve Using the Square Root Property x(2x-1)=17