Solve for x:
100 x^4-1261 x^2+441 = 0
Substitute y = x^2:
100 y^2-1261 y+441 = 0
The left hand side factors into a product with two terms:
(4 y-49) (25 y-9) = 0
Split into two equations:
4 y-49 = 0 or 25 y-9 = 0
Add 49 to both sides:
4 y = 49 or 25 y-9 = 0
Divide both sides by 4:
y = 49/4 or 25 y-9 = 0
Substitute back for y = x^2:
x^2 = 49/4 or 25 y-9 = 0
Take the square root of both sides:
x = 7/2 or x = -7/2 or 25 y-9 = 0
Add 9 to both sides:
x = 7/2 or x = -7/2 or 25 y = 9
Divide both sides by 25:
x = 7/2 or x = -7/2 or y = 9/25
Substitute back for y = x^2:
x = 7/2 or x = -7/2 or x^2 = 9/25
Take the square root of both sides:
Answer: | x = 7/2 or x = -7/2 or x = 3/5 or x = -3/5
Solve for x:
100 x^4-1261 x^2+441 = 0
Substitute y = x^2:
100 y^2-1261 y+441 = 0
The left hand side factors into a product with two terms:
(4 y-49) (25 y-9) = 0
Split into two equations:
4 y-49 = 0 or 25 y-9 = 0
Add 49 to both sides:
4 y = 49 or 25 y-9 = 0
Divide both sides by 4:
y = 49/4 or 25 y-9 = 0
Substitute back for y = x^2:
x^2 = 49/4 or 25 y-9 = 0
Take the square root of both sides:
x = 7/2 or x = -7/2 or 25 y-9 = 0
Add 9 to both sides:
x = 7/2 or x = -7/2 or 25 y = 9
Divide both sides by 25:
x = 7/2 or x = -7/2 or y = 9/25
Substitute back for y = x^2:
x = 7/2 or x = -7/2 or x^2 = 9/25
Take the square root of both sides:
Answer: | x = 7/2 or x = -7/2 or x = 3/5 or x = -3/5
+118723 How can you solve 100x^4-1261x^2+441=0
\(100x^4-1261x^2+441=0\\ let\;\;y=x^2\\ 100y^2-1261y+441=0\\ y=\frac{1261\pm\sqrt{1261^2-4*100*441}}{200}\\ y=\frac{1261\pm 1189}{200}\\ y=\frac{1261+1189}{200}\qquad or \qquad y=\frac{1261-1189}{200} \\ y=\frac{2450}{200}\qquad or \qquad y=\frac{72}{200} \\ y=\frac{1225}{100}\qquad or \qquad y=\frac{36}{100} \\ y=12.25 \qquad or \;\;\quad y=0.36 \\ x^2=12.25 \qquad or \;\;\quad x^2=0.36 \\ x=\pm3.5 \qquad or \;\;\quad x=\pm0.6 \\\)
