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

-2×2-5x+16=0
Factor -1 out of -2×2-5x+16.
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
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.
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
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 expression to solve for the + portion of the ±.
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
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 expression to solve for the – portion of the ±.
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
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