Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
x1=−21+7,x2=2−1+7
Alternative Form
x1≈−1.822876,x2≈0.822876
Evaluate
x2−3x2=∣2x−3∣
Simplify
More Steps
Evaluate
x2−3x2
Subtract the terms
More Steps
Simplify
x2−3x2
Collect like terms by calculating the sum or difference of their coefficients
(1−3)x2
Subtract the numbers
−2x2
−2x2
Rewrite the expression
2x2
When the expression in absolute value bars is not negative, remove the bars
2x2
2x2=∣2x−3∣
Swap the sides
∣2x−3∣=2x2
Rewrite the expression
∣2x−3∣−2x2=0
Separate the equation into 2 possible cases
2x−3−2x2=0,2x−3≥0−(2x−3)−2x2=0,2x−3<0
Solve the equation
More Steps
Evaluate
2x−3−2x2=0
Rewrite in standard form
−2x2+2x−3=0
Multiply both sides
2x2−2x+3=0
Substitute a=2,b=−2 and c=3 into the quadratic formula x=2a−b±b2−4ac
x=2×22±(−2)2−4×2×3
Simplify the expression
x=42±(−2)2−4×2×3
Simplify the expression
More Steps
Evaluate
(−2)2−4×2×3
Multiply the terms
(−2)2−24
Rewrite the expression
22−24
Evaluate the power
4−24
Subtract the numbers
−20
x=42±−20
The expression is undefined in the set of real numbers
x∈/R
x∈/R,2x−3≥0−(2x−3)−2x2=0,2x−3<0
Solve the inequality
More Steps
Evaluate
2x−3≥0
Move the constant to the right side
2x≥0+3
Removing 0 doesn't change the value,so remove it from the expression
2x≥3
Divide both sides
22x≥23
Divide the numbers
x≥23
x∈/R,x≥23−(2x−3)−2x2=0,2x−3<0
Solve the equation
More Steps
Evaluate
−(2x−3)−2x2=0
Calculate
−2x+3−2x2=0
Rewrite in standard form
−2x2−2x+3=0
Multiply both sides
2x2+2x−3=0
Substitute a=2,b=2 and c=−3 into the quadratic formula x=2a−b±b2−4ac
x=2×2−2±22−4×2(−3)
Simplify the expression
x=4−2±22−4×2(−3)
Simplify the expression
More Steps
Evaluate
22−4×2(−3)
Multiply
22−(−24)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
22+24
Evaluate the power
4+24
Add the numbers
28
x=4−2±28
Simplify the radical expression
More Steps
Evaluate
28
Write the expression as a product where the root of one of the factors can be evaluated
4×7
Write the number in exponential form with the base of 2
22×7
The root of a product is equal to the product of the roots of each factor
22×7
Reduce the index of the radical and exponent with 2
27
x=4−2±27
Separate the equation into 2 possible cases
x=4−2+27x=4−2−27
Simplify the expression
x=2−1+7x=4−2−27
Simplify the expression
x=2−1+7x=−21+7
x∈/R,x≥23x=2−1+7x=−21+7,2x−3<0
Solve the inequality
More Steps
Evaluate
2x−3<0
Move the constant to the right side
2x<0+3
Removing 0 doesn't change the value,so remove it from the expression
2x<3
Divide both sides
22x<23
Divide the numbers
x<23
x∈/R,x≥23x=2−1+7x=−21+7,x<23
Find the intersection
x∈/Rx=2−1+7x=−21+7,x<23
Find the intersection
x∈/Rx=2−1+7x=−21+7
Find the union
x=2−1+7x=−21+7
Solution
x1=−21+7,x2=2−1+7
Alternative Form
x1≈−1.822876,x2≈0.822876
Show Solution
Graph
