Question
Solve the quadratic equation
Solve using the quadratic formula
Solve by completing the square
Solve using the PQ formula
x1=260−3597,x2=260+3597
Alternative Form
x1≈0.012503,x2≈59.987497
Evaluate
3x(60−x)×80=180
Multiply the terms
240x(60−x)=180
Expand the expression
More Steps

Evaluate
240x(60−x)
Apply the distributive property
240x×60−240x×x
Multiply the numbers
14400x−240x×x
Multiply the terms
14400x−240x2
14400x−240x2=180
Move the expression to the left side
14400x−240x2−180=0
Rewrite in standard form
−240x2+14400x−180=0
Multiply both sides
240x2−14400x+180=0
Substitute a=240,b=−14400 and c=180 into the quadratic formula x=2a−b±b2−4ac
x=2×24014400±(−14400)2−4×240×180
Simplify the expression
x=48014400±(−14400)2−4×240×180
Simplify the expression
More Steps

Evaluate
(−14400)2−4×240×180
Multiply the terms
More Steps

Multiply the terms
4×240×180
Multiply the terms
960×180
Multiply the numbers
172800
(−14400)2−172800
Calculate
144002−172800
x=48014400±144002−172800
Simplify the radical expression
More Steps

Evaluate
144002−172800
Add the numbers
207187200
Write the expression as a product where the root of one of the factors can be evaluated
57600×3597
Write the number in exponential form with the base of 240
2402×3597
The root of a product is equal to the product of the roots of each factor
2402×3597
Reduce the index of the radical and exponent with 2
2403597
x=48014400±2403597
Separate the equation into 2 possible cases
x=48014400+2403597x=48014400−2403597
Simplify the expression
More Steps

Evaluate
x=48014400+2403597
Divide the terms
More Steps

Evaluate
48014400+2403597
Rewrite the expression
480240(60+3597)
Cancel out the common factor 240
260+3597
x=260+3597
x=260+3597x=48014400−2403597
Simplify the expression
More Steps

Evaluate
x=48014400−2403597
Divide the terms
More Steps

Evaluate
48014400−2403597
Rewrite the expression
480240(60−3597)
Cancel out the common factor 240
260−3597
x=260−3597
x=260+3597x=260−3597
Solution
x1=260−3597,x2=260+3597
Alternative Form
x1≈0.012503,x2≈59.987497
Show Solution
