Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
161x2−41x−411
Evaluate
161(x−2)2−3
Expand the expression
More Steps
Calculate
161(x−2)2
Simplify
161(x2−4x+4)
Apply the distributive property
161x2−161×4x+161×4
Multiply the numbers
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Evaluate
161×4
Reduce the numbers
41×1
Multiply the numbers
41
161x2−41x+161×4
Multiply the numbers
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Evaluate
161×4
Reduce the numbers
41×1
Multiply the numbers
41
161x2−41x+41
161x2−41x+41−3
Solution
More Steps
Evaluate
41−3
Reduce fractions to a common denominator
41−43×4
Write all numerators above the common denominator
41−3×4
Multiply the numbers
41−12
Subtract the numbers
4−11
Use b−a=−ba=−ba to rewrite the fraction
−411
161x2−41x−411
Show Solution
Factor the expression
161(x2−4x−44)
Evaluate
161(x−2)2−3
Simplify
More Steps
Evaluate
161(x−2)2
Simplify
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Evaluate
(x−2)2
Use (a−b)2=a2−2ab+b2 to expand the expression
x2−2x×2+22
Calculate
x2−4x+4
161(x2−4x+4)
Apply the distributive property
161x2+161(−4x)+161×4
Multiply the terms
More Steps
Evaluate
161(−4)
Multiplying or dividing an odd number of negative terms equals a negative
−161×4
Reduce the numbers
−41×1
Multiply the numbers
−41
161x2−41x+161×4
Multiply the terms
More Steps
Evaluate
161×4
Reduce the numbers
41×1
Multiply the numbers
41
161x2−41x+41
161x2−41x+41−3
Subtract the numbers
More Steps
Evaluate
41−3
Reduce fractions to a common denominator
41−43×4
Write all numerators above the common denominator
41−3×4
Multiply the numbers
41−12
Subtract the numbers
4−11
Use b−a=−ba=−ba to rewrite the fraction
−411
161x2−41x−411
Solution
161(x2−4x−44)
Show Solution
Find the roots
x1=−43+2,x2=43+2
Alternative Form
x1≈−4.928203,x2≈8.928203
Evaluate
(161)(x−2)2−3
To find the roots of the expression,set the expression equal to 0
(161)(x−2)2−3=0
Remove the unnecessary parentheses
161(x−2)2−3=0
Add or subtract both sides
161(x−2)2=0+3
Removing 0 doesn't change the value,so remove it from the expression
161(x−2)2=3
Multiply by the reciprocal
161(x−2)2×16=3×16
Multiply
(x−2)2=3×16
Multiply
(x−2)2=48
Take the root of both sides of the equation and remember to use both positive and negative roots
x−2=±48
Simplify the expression
More Steps
Evaluate
48
Write the expression as a product where the root of one of the factors can be evaluated
16×3
Write the number in exponential form with the base of 4
42×3
The root of a product is equal to the product of the roots of each factor
42×3
Reduce the index of the radical and exponent with 2
43
x−2=±43
Separate the equation into 2 possible cases
x−2=43x−2=−43
Move the constant to the right-hand side and change its sign
x=43+2x−2=−43
Move the constant to the right-hand side and change its sign
x=43+2x=−43+2
Solution
x1=−43+2,x2=43+2
Alternative Form
x1≈−4.928203,x2≈8.928203
Show Solution