Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
x=1
Evaluate
x∣x∣+7x−8=0
Separate the equation into 2 possible cases
x×x+7x−8=0,x≥0x(−x)+7x−8=0,x<0
Solve the equation
More Steps
Evaluate
x×x+7x−8=0
Calculate
x2+7x−8=0
Factor the expression
More Steps
Evaluate
x2+7x−8
Rewrite the expression
x2+(8−1)x−8
Calculate
x2+8x−x−8
Rewrite the expression
x×x+x×8−x−8
Factor out x from the expression
x(x+8)−x−8
Factor out −1 from the expression
x(x+8)−(x+8)
Factor out x+8 from the expression
(x−1)(x+8)
(x−1)(x+8)=0
When the product of factors equals 0,at least one factor is 0
x−1=0x+8=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+8=0
Solve the equation for x
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Evaluate
x+8=0
Move the constant to the right-hand side and change its sign
x=0−8
Removing 0 doesn't change the value,so remove it from the expression
x=−8
x=1x=−8
x=1x=−8,x≥0x(−x)+7x−8=0,x<0
Solve the equation
More Steps
Evaluate
x(−x)+7x−8=0
Calculate
−x×x+7x−8=0
Calculate
−x2+7x−8=0
Multiply both sides
x2−7x+8=0
Substitute a=1,b=−7 and c=8 into the quadratic formula x=2a−b±b2−4ac
x=27±(−7)2−4×8
Simplify the expression
More Steps
Evaluate
(−7)2−4×8
Multiply the numbers
(−7)2−32
Rewrite the expression
72−32
Evaluate the power
49−32
Subtract the numbers
17
x=27±17
Separate the equation into 2 possible cases
x=27+17x=27−17
x=1x=−8,x≥0x=27+17x=27−17,x<0
Find the intersection
x=1x=27+17x=27−17,x<0
Find the intersection
x=1x∈∅
Solution
x=1
Show Solution
Graph
