Graph 4x^2+4y^2-24x+8x<-39

Math
4×2+4y2-24x+8x<-39
Solve for y.
Tap for more steps…
Add -24x and 8x.
4×2+4y2-16x<-39
Move all terms not containing y to the right side of the inequality.
Tap for more steps…
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.
Tap for more steps…
Divide each term in 4y2<-39-4×2+16x by 4.
4y24<-394+-4×24+16×4
Cancel the common factor of 4.
Tap for more steps…
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.
Tap for more steps…
Move the negative in front of the fraction.
y2<-394+-4×24+16×4
Cancel the common factor of -4 and 4.
Tap for more steps…
Factor 4 out of -4×2.
y2<-394+4(-x2)4+16×4
Cancel the common factors.
Tap for more steps…
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.
Tap for more steps…
Factor 4 out of 16x.
y2<-394-x2+4(4x)4
Cancel the common factors.
Tap for more steps…
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.
Tap for more steps…
Simplify the right side of the equation.
Tap for more steps…
Let u=-1. Substitute u for all occurrences of -1.
Tap for more steps…
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.
Tap for more steps…
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).
Tap for more steps…
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.
Tap for more steps…
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
Graph 4x^2+4y^2-24x+8x<-39

Download our
App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Scroll to top