-2×2-5x+16=0

Factor -1 out of -2×2.

-(2×2)-5x+16=0

Factor -1 out of -5x.

-(2×2)-(5x)+16=0

Rewrite 16 as -1(-16).

-(2×2)-(5x)-1⋅-16=0

Factor -1 out of -(2×2)-(5x).

-(2×2+5x)-1⋅-16=0

Factor -1 out of -(2×2+5x)-1(-16).

-(2×2+5x-16)=0

-(2×2+5x-16)=0

Multiply each term in -(2×2+5x-16)=0 by -1.

-(2×2+5x-16)⋅-1=0⋅-1

Simplify -(2×2+5x-16)⋅-1.

Apply the distributive property.

(-(2×2)-(5x)–16)⋅-1=0⋅-1

Simplify.

Multiply 2 by -1.

(-2×2-(5x)–16)⋅-1=0⋅-1

Multiply 5 by -1.

(-2×2-5x–16)⋅-1=0⋅-1

Multiply -1 by -16.

(-2×2-5x+16)⋅-1=0⋅-1

(-2×2-5x+16)⋅-1=0⋅-1

Apply the distributive property.

-2×2⋅-1-5x⋅-1+16⋅-1=0⋅-1

Simplify.

Multiply -1 by -2.

2×2-5x⋅-1+16⋅-1=0⋅-1

Multiply -1 by -5.

2×2+5x+16⋅-1=0⋅-1

Multiply 16 by -1.

2×2+5x-16=0⋅-1

2×2+5x-16=0⋅-1

2×2+5x-16=0⋅-1

Multiply 0 by -1.

2×2+5x-16=0

2×2+5x-16=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=2, b=5, and c=-16 into the quadratic formula and solve for x.

-5±52-4⋅(2⋅-16)2⋅2

Simplify the numerator.

Raise 5 to the power of 2.

x=-5±25-4⋅(2⋅-16)2⋅2

Multiply 2 by -16.

x=-5±25-4⋅-322⋅2

Multiply -4 by -32.

x=-5±25+1282⋅2

Add 25 and 128.

x=-5±1532⋅2

Rewrite 153 as 32⋅17.

Factor 9 out of 153.

x=-5±9(17)2⋅2

Rewrite 9 as 32.

x=-5±32⋅172⋅2

x=-5±32⋅172⋅2

Pull terms out from under the radical.

x=-5±3172⋅2

x=-5±3172⋅2

Multiply 2 by 2.

x=-5±3174

x=-5±3174

Simplify the numerator.

Raise 5 to the power of 2.

x=-5±25-4⋅(2⋅-16)2⋅2

Multiply 2 by -16.

x=-5±25-4⋅-322⋅2

Multiply -4 by -32.

x=-5±25+1282⋅2

Add 25 and 128.

x=-5±1532⋅2

Rewrite 153 as 32⋅17.

Factor 9 out of 153.

x=-5±9(17)2⋅2

Rewrite 9 as 32.

x=-5±32⋅172⋅2

x=-5±32⋅172⋅2

Pull terms out from under the radical.

x=-5±3172⋅2

x=-5±3172⋅2

Multiply 2 by 2.

x=-5±3174

Change the ± to +.

x=-5+3174

Rewrite -5 as -1(5).

x=-1⋅5+3174

Factor -1 out of 317.

x=-1⋅5-(-317)4

Factor -1 out of -1(5)-(-317).

x=-1(5-317)4

Move the negative in front of the fraction.

x=-5-3174

x=-5-3174

Simplify the numerator.

Raise 5 to the power of 2.

x=-5±25-4⋅(2⋅-16)2⋅2

Multiply 2 by -16.

x=-5±25-4⋅-322⋅2

Multiply -4 by -32.

x=-5±25+1282⋅2

Add 25 and 128.

x=-5±1532⋅2

Rewrite 153 as 32⋅17.

Factor 9 out of 153.

x=-5±9(17)2⋅2

Rewrite 9 as 32.

x=-5±32⋅172⋅2

x=-5±32⋅172⋅2

Pull terms out from under the radical.

x=-5±3172⋅2

x=-5±3172⋅2

Multiply 2 by 2.

x=-5±3174

Change the ± to -.

x=-5-3174

Rewrite -5 as -1(5).

x=-1⋅5-3174

Factor -1 out of -317.

x=-1⋅5-(317)4

Factor -1 out of -1(5)-(317).

x=-1(5+317)4

Move the negative in front of the fraction.

x=-5+3174

x=-5+3174

The final answer is the combination of both solutions.

x=-5-3174,-5+3174

The result can be shown in multiple forms.

Exact Form:

x=-5-3174,-5+3174

Decimal Form:

x=1.84232921…,-4.34232921…

Solve Using the Square Root Property -2x^2-5x+16=0