Question
Solve the quadratic equation
Solve using the quadratic formula
Solve by completing the square
Solve using the PQ formula
s1=3045−1155,s2=3045+1155
Alternative Form
s1≈0.367157,s2≈2.632843
Evaluate
−10(s−3)×6s=58
Multiply
More Steps

Evaluate
−10(s−3)×6s
Multiply the terms
−60(s−3)s
Multiply the terms
−60s(s−3)
−60s(s−3)=58
Expand the expression
More Steps

Evaluate
−60s(s−3)
Apply the distributive property
−60s×s−(−60s×3)
Multiply the terms
−60s2−(−60s×3)
Multiply the numbers
−60s2−(−180s)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−60s2+180s
−60s2+180s=58
Move the expression to the left side
−60s2+180s−58=0
Multiply both sides
60s2−180s+58=0
Substitute a=60,b=−180 and c=58 into the quadratic formula s=2a−b±b2−4ac
s=2×60180±(−180)2−4×60×58
Simplify the expression
s=120180±(−180)2−4×60×58
Simplify the expression
More Steps

Evaluate
(−180)2−4×60×58
Multiply the terms
More Steps

Multiply the terms
4×60×58
Multiply the terms
240×58
Multiply the numbers
13920
(−180)2−13920
Rewrite the expression
1802−13920
Evaluate the power
32400−13920
Subtract the numbers
18480
s=120180±18480
Simplify the radical expression
More Steps

Evaluate
18480
Write the expression as a product where the root of one of the factors can be evaluated
16×1155
Write the number in exponential form with the base of 4
42×1155
The root of a product is equal to the product of the roots of each factor
42×1155
Reduce the index of the radical and exponent with 2
41155
s=120180±41155
Separate the equation into 2 possible cases
s=120180+41155s=120180−41155
Simplify the expression
More Steps

Evaluate
s=120180+41155
Divide the terms
More Steps

Evaluate
120180+41155
Rewrite the expression
1204(45+1155)
Cancel out the common factor 4
3045+1155
s=3045+1155
s=3045+1155s=120180−41155
Simplify the expression
More Steps

Evaluate
s=120180−41155
Divide the terms
More Steps

Evaluate
120180−41155
Rewrite the expression
1204(45−1155)
Cancel out the common factor 4
3045−1155
s=3045−1155
s=3045+1155s=3045−1155
Solution
s1=3045−1155,s2=3045+1155
Alternative Form
s1≈0.367157,s2≈2.632843
Show Solution
