Algebra
Calculus
Trigonometry
Matrix
Question
Solve the quadratic equation
Solve using the quadratic formula
Solve by completing the square
Solve using the PQ formula
x1=−1−13,x2=−1+13
Alternative Form
x1≈−4.605551,x2≈2.605551
Evaluate
4−32x=3x2
Swap the sides
3x2=4−32x
Rewrite the expression
31x2=4−32x
Move the expression to the left side
31x2−4+32x=0
Rewrite in standard form
31x2+32x−4=0
Multiply both sides
3(31x2+32x−4)=3×0
Calculate
x2+2x−12=0
Substitute a=1,b=2 and c=−12 into the quadratic formula x=2a−b±b2−4ac
x=2−2±22−4(−12)
Simplify the expression
More Steps
Evaluate
22−4(−12)
Multiply the numbers
More Steps
Evaluate
4(−12)
Multiplying or dividing an odd number of negative terms equals a negative
−4×12
Multiply the numbers
−48
22−(−48)
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+48
Evaluate the power
4+48
Add the numbers
52
x=2−2±52
Simplify the radical expression
More Steps
Evaluate
52
Write the expression as a product where the root of one of the factors can be evaluated
4×13
Write the number in exponential form with the base of 2
22×13
The root of a product is equal to the product of the roots of each factor
22×13
Reduce the index of the radical and exponent with 2
213
x=2−2±213
Separate the equation into 2 possible cases
x=2−2+213x=2−2−213
Simplify the expression
More Steps
Evaluate
x=2−2+213
Divide the terms
More Steps
Evaluate
2−2+213
Rewrite the expression
22(−1+13)
Reduce the fraction
−1+13
x=−1+13
x=−1+13x=2−2−213
Simplify the expression
More Steps
Evaluate
x=2−2−213
Divide the terms
More Steps
Evaluate
2−2−213
Rewrite the expression
22(−1−13)
Reduce the fraction
−1−13
x=−1−13
x=−1+13x=−1−13
Solution
x1=−1−13,x2=−1+13
Alternative Form
x1≈−4.605551,x2≈2.605551
Show Solution
Graph
