Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
5x2+16x−16
Evaluate
(3x×1)2−4(x−2)2
Multiply the terms
(3x)2−4(x−2)2
Rewrite the expression
9x2−4(x−2)2
Expand the expression
More Steps
Calculate
−4(x−2)2
Simplify
−4(x2−4x+4)
Apply the distributive property
−4x2−(−4×4x)−4×4
Multiply the numbers
−4x2−(−16x)−4×4
Multiply the numbers
−4x2−(−16x)−16
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−4x2+16x−16
9x2−4x2+16x−16
Solution
More Steps
Evaluate
9x2−4x2
Collect like terms by calculating the sum or difference of their coefficients
(9−4)x2
Subtract the numbers
5x2
5x2+16x−16
Show Solution
Factor the expression
(5x−4)(x+4)
Evaluate
(3x×1)2−4(x−2)2
Multiply the terms
(3x)2−4(x−2)2
Use a2−b2=(a−b)(a+b) to factor the expression
((3x)+2(x−2))((3x)−2(x−2))
Solution
(5x−4)(x+4)
Show Solution
Find the roots
x1=−4,x2=54
Alternative Form
x1=−4,x2=0.8
Evaluate
(3x×1)2−4(x−2)2
To find the roots of the expression,set the expression equal to 0
(3x×1)2−4(x−2)2=0
Multiply the terms
(3x)2−4(x−2)2=0
Rewrite the expression
More Steps
Simplify
(3x)2−4(x−2)2
Rewrite the expression
More Steps
Evaluate
(3x)2
To raise a product to a power,raise each factor to that power
32x2
Evaluate the power
9x2
9x2−4(x−2)2
9x2−4(x−2)2=0
Calculate
More Steps
Evaluate
9x2−4(x−2)2
Expand the expression
More Steps
Calculate
−4(x−2)2
Simplify
−4(x2−4x+4)
Apply the distributive property
−4x2−(−4×4x)−4×4
Multiply the numbers
−4x2−(−16x)−4×4
Multiply the numbers
−4x2−(−16x)−16
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−4x2+16x−16
9x2−4x2+16x−16
Subtract the terms
More Steps
Evaluate
9x2−4x2
Collect like terms by calculating the sum or difference of their coefficients
(9−4)x2
Subtract the numbers
5x2
5x2+16x−16
5x2+16x−16=0
Factor the expression
More Steps
Evaluate
5x2+16x−16
Rewrite the expression
5x2+(−4+20)x−16
Calculate
5x2−4x+20x−16
Rewrite the expression
x×5x−x×4+4×5x−4×4
Factor out x from the expression
x(5x−4)+4×5x−4×4
Factor out 4 from the expression
x(5x−4)+4(5x−4)
Factor out 5x−4 from the expression
(x+4)(5x−4)
(x+4)(5x−4)=0
When the product of factors equals 0,at least one factor is 0
x+4=05x−4=0
Solve the equation for x
More Steps
Evaluate
x+4=0
Move the constant to the right-hand side and change its sign
x=0−4
Removing 0 doesn't change the value,so remove it from the expression
x=−4
x=−45x−4=0
Solve the equation for x
More Steps
Evaluate
5x−4=0
Move the constant to the right-hand side and change its sign
5x=0+4
Removing 0 doesn't change the value,so remove it from the expression
5x=4
Divide both sides
55x=54
Divide the numbers
x=54
x=−4x=54
Solution
x1=−4,x2=54
Alternative Form
x1=−4,x2=0.8
Show Solution