Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
x2+2x−7
Evaluate
(x−2)(x+4)+1
Expand the expression
More Steps
Calculate
(x−2)(x+4)
Apply the distributive property
x×x+x×4−2x−2×4
Multiply the terms
x2+x×4−2x−2×4
Use the commutative property to reorder the terms
x2+4x−2x−2×4
Multiply the numbers
x2+4x−2x−8
Subtract the terms
More Steps
Evaluate
4x−2x
Collect like terms by calculating the sum or difference of their coefficients
(4−2)x
Subtract the numbers
2x
x2+2x−8
x2+2x−8+1
Solution
x2+2x−7
Show Solution
Find the roots
x1=−1−22,x2=−1+22
Alternative Form
x1≈−3.828427,x2≈1.828427
Evaluate
(x−2)(x+4)+1
To find the roots of the expression,set the expression equal to 0
(x−2)(x+4)+1=0
Calculate
More Steps
Evaluate
(x−2)(x+4)+1
Expand the expression
More Steps
Calculate
(x−2)(x+4)
Apply the distributive property
x×x+x×4−2x−2×4
Multiply the terms
x2+x×4−2x−2×4
Use the commutative property to reorder the terms
x2+4x−2x−2×4
Multiply the numbers
x2+4x−2x−8
Subtract the terms
x2+2x−8
x2+2x−8+1
Add the numbers
x2+2x−7
x2+2x−7=0
Substitute a=1,b=2 and c=−7 into the quadratic formula x=2a−b±b2−4ac
x=2−2±22−4(−7)
Simplify the expression
More Steps
Evaluate
22−4(−7)
Multiply the numbers
More Steps
Evaluate
4(−7)
Multiplying or dividing an odd number of negative terms equals a negative
−4×7
Multiply the numbers
−28
22−(−28)
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+28
Evaluate the power
4+28
Add the numbers
32
x=2−2±32
Simplify the radical expression
More Steps
Evaluate
32
Write the expression as a product where the root of one of the factors can be evaluated
16×2
Write the number in exponential form with the base of 4
42×2
The root of a product is equal to the product of the roots of each factor
42×2
Reduce the index of the radical and exponent with 2
42
x=2−2±42
Separate the equation into 2 possible cases
x=2−2+42x=2−2−42
Simplify the expression
More Steps
Evaluate
x=2−2+42
Divide the terms
More Steps
Evaluate
2−2+42
Rewrite the expression
22(−1+22)
Reduce the fraction
−1+22
x=−1+22
x=−1+22x=2−2−42
Simplify the expression
More Steps
Evaluate
x=2−2−42
Divide the terms
More Steps
Evaluate
2−2−42
Rewrite the expression
22(−1−22)
Reduce the fraction
−1−22
x=−1−22
x=−1+22x=−1−22
Solution
x1=−1−22,x2=−1+22
Alternative Form
x1≈−3.828427,x2≈1.828427
Show Solution