Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
x=105+145
Alternative Form
x≈1.704159
Evaluate
6−∣x−1∣×5x=0
Multiply the first two terms
6−5∣x−1∣×x=0
Separate the equation into 2 possible cases
6−5(x−1)x=0,x−1≥06−5(−(x−1))x=0,x−1<0
Solve the equation
More Steps
Evaluate
6−5(x−1)x=0
Calculate
More Steps
Calculate
−5(x−1)x
Simplify
(−5x+5)x
Apply the distributive property
−5x×x+5x
Multiply the terms
−5x2+5x
6−5x2+5x=0
Rewrite in standard form
−5x2+5x+6=0
Multiply both sides
5x2−5x−6=0
Substitute a=5,b=−5 and c=−6 into the quadratic formula x=2a−b±b2−4ac
x=2×55±(−5)2−4×5(−6)
Simplify the expression
x=105±(−5)2−4×5(−6)
Simplify the expression
More Steps
Evaluate
(−5)2−4×5(−6)
Multiply
(−5)2−(−120)
Rewrite the expression
52−(−120)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
52+120
Evaluate the power
25+120
Add the numbers
145
x=105±145
Separate the equation into 2 possible cases
x=105+145x=105−145
x=105+145x=105−145,x−1≥06−5(−(x−1))x=0,x−1<0
Solve the inequality
More Steps
Evaluate
x−1≥0
Move the constant to the right side
x≥0+1
Removing 0 doesn't change the value,so remove it from the expression
x≥1
x=105+145x=105−145,x≥16−5(−(x−1))x=0,x−1<0
Solve the equation
More Steps
Evaluate
6−5(−(x−1))x=0
Calculate
6−5(−x+1)x=0
Calculate
More Steps
Calculate
−5(−x+1)x
Simplify
(5x−5)x
Apply the distributive property
5x×x−5x
Multiply the terms
5x2−5x
6+5x2−5x=0
Rewrite in standard form
5x2−5x+6=0
Substitute a=5,b=−5 and c=6 into the quadratic formula x=2a−b±b2−4ac
x=2×55±(−5)2−4×5×6
Simplify the expression
x=105±(−5)2−4×5×6
Simplify the expression
More Steps
Evaluate
(−5)2−4×5×6
Multiply the terms
(−5)2−120
Rewrite the expression
52−120
Evaluate the power
25−120
Subtract the numbers
−95
x=105±−95
The expression is undefined in the set of real numbers
x∈/R
x=105+145x=105−145,x≥1x∈/R,x−1<0
Solve the inequality
More Steps
Evaluate
x−1<0
Move the constant to the right side
x<0+1
Removing 0 doesn't change the value,so remove it from the expression
x<1
x=105+145x=105−145,x≥1x∈/R,x<1
Find the intersection
x=105+145x∈/R,x<1
Find the intersection
x=105+145x∈/R
Solution
x=105+145
Alternative Form
x≈1.704159
Show Solution
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