Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
x1=−4,x2=4
Evaluate
x2−3∣x∣−4=0
Separate the equation into 2 possible cases
x2−3x−4=0,x≥0x2−3(−x)−4=0,x<0
Solve the equation
More Steps
Evaluate
x2−3x−4=0
Factor the expression
More Steps
Evaluate
x2−3x−4
Rewrite the expression
x2+(1−4)x−4
Calculate
x2+x−4x−4
Rewrite the expression
x×x+x−4x−4
Factor out x from the expression
x(x+1)−4x−4
Factor out −4 from the expression
x(x+1)−4(x+1)
Factor out x+1 from the expression
(x−4)(x+1)
(x−4)(x+1)=0
When the product of factors equals 0,at least one factor is 0
x−4=0x+1=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=4x+1=0
Solve the equation for x
More Steps
Evaluate
x+1=0
Move the constant to the right-hand side and change its sign
x=0−1
Removing 0 doesn't change the value,so remove it from the expression
x=−1
x=4x=−1
x=4x=−1,x≥0x2−3(−x)−4=0,x<0
Solve the equation
More Steps
Evaluate
x2−3(−x)−4=0
Calculate
x2+3x−4=0
Factor the expression
More Steps
Evaluate
x2+3x−4
Rewrite the expression
x2+(4−1)x−4
Calculate
x2+4x−x−4
Rewrite the expression
x×x+x×4−x−4
Factor out x from the expression
x(x+4)−x−4
Factor out −1 from the expression
x(x+4)−(x+4)
Factor out x+4 from the expression
(x−1)(x+4)
(x−1)(x+4)=0
When the product of factors equals 0,at least one factor is 0
x−1=0x+4=0
Solve the equation for x
More Steps
Evaluate
x−1=0
Move the constant to the right-hand side and change its sign
x=0+1
Removing 0 doesn't change the value,so remove it from the expression
x=1
x=1x+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=1x=−4
x=4x=−1,x≥0x=1x=−4,x<0
Find the intersection
x=4x=1x=−4,x<0
Find the intersection
x=4x=−4
Solution
x1=−4,x2=4
Show Solution
Graph
