Question
Solve the quadratic equation
Solve using the quadratic formula
Solve by completing the square
Solve using the PQ formula
q1=11911−1787,q2=11911+1787
Alternative Form
q1≈−0.262798,q2≈0.447672
Evaluate
7q×17q−14q−8q=14
Simplify
More Steps

Evaluate
7q×17q−14q−8q
Multiply
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Multiply the terms
7q×17q
Multiply the terms
119q×q
Multiply the terms
119q2
119q2−14q−8q
Subtract the terms
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Evaluate
−14q−8q
Collect like terms by calculating the sum or difference of their coefficients
(−14−8)q
Subtract the numbers
−22q
119q2−22q
119q2−22q=14
Move the expression to the left side
119q2−22q−14=0
Substitute a=119,b=−22 and c=−14 into the quadratic formula q=2a−b±b2−4ac
q=2×11922±(−22)2−4×119(−14)
Simplify the expression
q=23822±(−22)2−4×119(−14)
Simplify the expression
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Evaluate
(−22)2−4×119(−14)
Multiply
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Multiply the terms
4×119(−14)
Rewrite the expression
−4×119×14
Multiply the terms
−6664
(−22)2−(−6664)
Rewrite the expression
222−(−6664)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
222+6664
Evaluate the power
484+6664
Add the numbers
7148
q=23822±7148
Simplify the radical expression
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Evaluate
7148
Write the expression as a product where the root of one of the factors can be evaluated
4×1787
Write the number in exponential form with the base of 2
22×1787
The root of a product is equal to the product of the roots of each factor
22×1787
Reduce the index of the radical and exponent with 2
21787
q=23822±21787
Separate the equation into 2 possible cases
q=23822+21787q=23822−21787
Simplify the expression
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Evaluate
q=23822+21787
Divide the terms
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Evaluate
23822+21787
Rewrite the expression
2382(11+1787)
Cancel out the common factor 2
11911+1787
q=11911+1787
q=11911+1787q=23822−21787
Simplify the expression
More Steps

Evaluate
q=23822−21787
Divide the terms
More Steps

Evaluate
23822−21787
Rewrite the expression
2382(11−1787)
Cancel out the common factor 2
11911−1787
q=11911−1787
q=11911+1787q=11911−1787
Solution
q1=11911−1787,q2=11911+1787
Alternative Form
q1≈−0.262798,q2≈0.447672
Show Solution
