# Solve Using the Square Root Property x^2-3/2x-27/16=0

x2-32x-2716=0
Simplify each term.
Combine x and 32.
x2-x⋅32-2716=0
Move 3 to the left of x.
x2-3×2-2716=0
x2-3×2-2716=0
Multiply through by the least common denominator 16, then simplify.
Apply the distributive property.
16×2+16(-3×2)+16(-2716)=0
Simplify.
Cancel the common factor of 2.
Move the leading negative in -3×2 into the numerator.
16×2+16(-3×2)+16(-2716)=0
Factor 2 out of 16.
16×2+2(8)(-3×2)+16(-2716)=0
Cancel the common factor.
16×2+2⋅(8(-3×2))+16(-2716)=0
Rewrite the expression.
16×2+8(-3x)+16(-2716)=0
16×2+8(-3x)+16(-2716)=0
Multiply -3 by 8.
16×2-24x+16(-2716)=0
Cancel the common factor of 16.
Move the leading negative in -2716 into the numerator.
16×2-24x+16(-2716)=0
Cancel the common factor.
16×2-24x+16(-2716)=0
Rewrite the expression.
16×2-24x-27=0
16×2-24x-27=0
16×2-24x-27=0
16×2-24x-27=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=16, b=-24, and c=-27 into the quadratic formula and solve for x.
24±(-24)2-4⋅(16⋅-27)2⋅16
Simplify.
Simplify the numerator.
Raise -24 to the power of 2.
x=24±576-4⋅(16⋅-27)2⋅16
Multiply 16 by -27.
x=24±576-4⋅-4322⋅16
Multiply -4 by -432.
x=24±576+17282⋅16
x=24±23042⋅16
Rewrite 2304 as 482.
x=24±4822⋅16
Pull terms out from under the radical, assuming positive real numbers.
x=24±482⋅16
x=24±482⋅16
Multiply 2 by 16.
x=24±4832
Simplify 24±4832.
x=3±64
x=3±64
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
Raise -24 to the power of 2.
x=24±576-4⋅(16⋅-27)2⋅16
Multiply 16 by -27.
x=24±576-4⋅-4322⋅16
Multiply -4 by -432.
x=24±576+17282⋅16
x=24±23042⋅16
Rewrite 2304 as 482.
x=24±4822⋅16
Pull terms out from under the radical, assuming positive real numbers.
x=24±482⋅16
x=24±482⋅16
Multiply 2 by 16.
x=24±4832
Simplify 24±4832.
x=3±64
Change the ± to +.
x=3+64
x=94
x=94
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
Raise -24 to the power of 2.
x=24±576-4⋅(16⋅-27)2⋅16
Multiply 16 by -27.
x=24±576-4⋅-4322⋅16
Multiply -4 by -432.
x=24±576+17282⋅16
x=24±23042⋅16
Rewrite 2304 as 482.
x=24±4822⋅16
Pull terms out from under the radical, assuming positive real numbers.
x=24±482⋅16
x=24±482⋅16
Multiply 2 by 16.
x=24±4832
Simplify 24±4832.
x=3±64
Change the ± to -.
x=3-64
Subtract 6 from 3.
x=-34
Move the negative in front of the fraction.
x=-34
x=-34
The final answer is the combination of both solutions.
x=94,-34
Solve Using the Square Root Property x^2-3/2x-27/16=0