4×2+4y2-24x+8x<-39
Add -24x and 8x.
4×2+4y2-16x<-39
Move all terms not containing y to the right side of the inequality.
Subtract 4×2 from both sides of the inequality.
4y2-16x<-39-4×2
Add 16x to both sides of the inequality.
4y2<-39-4×2+16x
4y2<-39-4×2+16x
Divide each term by 4 and simplify.
Divide each term in 4y2<-39-4×2+16x by 4.
4y24<-394+-4×24+16×4
Cancel the common factor of 4.
Cancel the common factor.
4y24<-394+-4×24+16×4
Divide y2 by 1.
y2<-394+-4×24+16×4
y2<-394+-4×24+16×4
Simplify each term.
Move the negative in front of the fraction.
y2<-394+-4×24+16×4
Cancel the common factor of -4 and 4.
Factor 4 out of -4×2.
y2<-394+4(-x2)4+16×4
Cancel the common factors.
Factor 4 out of 4.
y2<-394+4(-x2)4(1)+16×4
Cancel the common factor.
y2<-394+4(-x2)4⋅1+16×4
Rewrite the expression.
y2<-394+-x21+16×4
Divide -x2 by 1.
y2<-394-x2+16×4
y2<-394-x2+16×4
y2<-394-x2+16×4
Cancel the common factor of 16 and 4.
Factor 4 out of 16x.
y2<-394-x2+4(4x)4
Cancel the common factors.
Factor 4 out of 4.
y2<-394-x2+4(4x)4(1)
Cancel the common factor.
y2<-394-x2+4(4x)4⋅1
Rewrite the expression.
y2<-394-x2+4×1
Divide 4x by 1.
y2<-394-x2+4x
y2<-394-x2+4x
y2<-394-x2+4x
y2<-394-x2+4x
y2<-394-x2+4x
Take the square root of both sides of the inequality to eliminate the exponent on the left side.
y<±-394-x2+4x
The complete solution is the result of both the positive and negative portions of the solution.
Simplify the right side of the equation.
Let u=-1. Substitute u for all occurrences of -1.
Apply the distributive property.
y<±u⋅39+u(4×2)+4x⋅44
Move 39 to the left of u.
y<±39⋅u+u(4×2)+4x⋅44
Rewrite using the commutative property of multiplication.
y<±39⋅u+4ux2+4x⋅44
Multiply 4 by 4.
y<±39u+4ux2+16×4
y<±39u+4ux2+16×4
Replace all occurrences of u with -1.
y<±39⋅-1+4⋅(-1×2)+16×4
Simplify each term.
Multiply 39 by -1.
y<±-39+4⋅(-1×2)+16×4
Multiply 4 by -1.
y<±-39-4×2+16×4
y<±-39-4×2+16×4
Reorder terms.
y<±-4×2+16x-394
Rewrite -4×2+16x-394 as (12)2(-4×2+16x-39).
Factor the perfect power 12 out of -4×2+16x-39.
y<±12(-4×2+16x-39)4
Factor the perfect power 22 out of 4.
y<±12(-4×2+16x-39)22⋅1
Rearrange the fraction 12(-4×2+16x-39)22⋅1.
y<±(12)2(-4×2+16x-39)
y<±(12)2(-4×2+16x-39)
Pull terms out from under the radical.
y<±12⋅-4×2+16x-39
Combine 12 and -4×2+16x-39.
y<±-4×2+16x-392
y<±-4×2+16x-392
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the ± to find the first solution.
y<-4×2+16x-392
Next, use the negative value of the ± to find the second solution. Since this is an inequality, flip the direction of the inequality sign on the – portion of the solution.
y>–4×2+16x-392
The complete solution is the result of both the positive and negative portions of the solution.
y<-4×2+16x-392 and y>–4×2+16x-392
Find the intersection.
–4×2+16x-392<y<-4×2+16x-392
–4×2+16x-392<y<-4×2+16x-392
–4×2+16x-392<y<-4×2+16x-392
–4×2+16x-392<y<-4×2+16x-392
The equation is not linear, so the slope does not exist.
Not Linear
Graph a dashed line, then shade the area below the boundary line since y is less than .
–4×2+16x-392<y<-4×2+16x-392
<div data-graph-input="{"graphs":[{"ascii":"-(\sqrt(-4x^(2)+16x-39))/(2)<y
