Question
Solve the quadratic equation
Solve using the quadratic formula
Solve by completing the square
Solve using the PQ formula
d1=615−205,d2=615+205
Alternative Form
d1≈0.113696,d2≈4.886304
Evaluate
−15=3(d−5)×9d
Multiply
More Steps

Evaluate
3(d−5)×9d
Multiply the terms
27(d−5)d
Multiply the terms
27d(d−5)
−15=27d(d−5)
Swap the sides
27d(d−5)=−15
Expand the expression
More Steps

Evaluate
27d(d−5)
Apply the distributive property
27d×d−27d×5
Multiply the terms
27d2−27d×5
Multiply the numbers
27d2−135d
27d2−135d=−15
Move the expression to the left side
27d2−135d+15=0
Substitute a=27,b=−135 and c=15 into the quadratic formula d=2a−b±b2−4ac
d=2×27135±(−135)2−4×27×15
Simplify the expression
d=54135±(−135)2−4×27×15
Simplify the expression
More Steps

Evaluate
(−135)2−4×27×15
Multiply the terms
More Steps

Multiply the terms
4×27×15
Multiply the terms
108×15
Multiply the numbers
1620
(−135)2−1620
Rewrite the expression
1352−1620
Evaluate the power
18225−1620
Subtract the numbers
16605
d=54135±16605
Simplify the radical expression
More Steps

Evaluate
16605
Write the expression as a product where the root of one of the factors can be evaluated
81×205
Write the number in exponential form with the base of 9
92×205
The root of a product is equal to the product of the roots of each factor
92×205
Reduce the index of the radical and exponent with 2
9205
d=54135±9205
Separate the equation into 2 possible cases
d=54135+9205d=54135−9205
Simplify the expression
More Steps

Evaluate
d=54135+9205
Divide the terms
More Steps

Evaluate
54135+9205
Rewrite the expression
549(15+205)
Cancel out the common factor 9
615+205
d=615+205
d=615+205d=54135−9205
Simplify the expression
More Steps

Evaluate
d=54135−9205
Divide the terms
More Steps

Evaluate
54135−9205
Rewrite the expression
549(15−205)
Cancel out the common factor 9
615−205
d=615−205
d=615+205d=615−205
Solution
d1=615−205,d2=615+205
Alternative Form
d1≈0.113696,d2≈4.886304
Show Solution
