# Solve Using the Square Root Property x(2x-1)=17 x(2x-1)=17
Simplify x(2x-1).
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.
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 expression to solve for the + portion of the ±.
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 expression to solve for the – portion of the ±.
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…
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