Solve r^2-r-20=0 - ScanMath

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

r_{1} = - 4, r_{2} = 5

Evaluate

r^{2} - r - 20 = 0

Factor the expression

More Steps

Evaluate

r^{2} - r - 20

Rewrite the expression

r^{2} + (4 - 5) r - 20

Calculate

r^{2} + 4 r - 5 r - 20

Rewrite the expression

r \times r + r \times 4 - 5 r - 5 \times 4

Factor out r from the expression

r (r + 4) - 5 r - 5 \times 4

Factor out - 5 from the expression

r (r + 4) - 5 (r + 4)

Factor out r + 4 from the expression

(r - 5) (r + 4)

(r - 5) (r + 4) = 0

When the product of factors equals 0,at least one factor is 0

r - 5 = 0 r + 4 = 0

Solve the equation for r

More Steps

Evaluate

r - 5 = 0

Move the constant to the right-hand side and change its sign

r = 0 + 5

Removing 0 doesn't change the value,so remove it from the expression

r = 5

r = 5 r + 4 = 0

Solve the equation for r

More Steps

Evaluate

r + 4 = 0

Move the constant to the right-hand side and change its sign

r = 0 - 4

Removing 0 doesn't change the value,so remove it from the expression

r = - 4

r = 5 r = - 4

Solution

r_{1} = - 4, r_{2} = 5

Show Solution

41 x^{2} + 41 y^{2} = x^{4} + y^{4} + 400 + 2 x^{2} y^{2}

Evaluate

r^{2} - r - 20 = 0

Rewrite the expression

r^{2} - r = 20

To covert the equation to rectangular coordinates using conversion formulas,substitute x^{2} + y^{2} for r^{2}

x^{2} + y^{2} - r = 20

Simplify the expression

- r = - x^{2} - y^{2} + 20

Square both sides of the equation

(- r)^{2} = (- x^{2} - y^{2} + 20)^{2}

To covert the equation to rectangular coordinates using conversion formulas,substitute x^{2} + y^{2} for r^{2}

x^{2} + y^{2} = (- x^{2} - y^{2} + 20)^{2}

Calculate

x^{2} + y^{2} = x^{4} + y^{4} + 400 + 2 x^{2} y^{2} - 40 x^{2} - 40 y^{2}

Move the expression to the left side

x^{2} + y^{2} - (- 40 x^{2} - 40 y^{2}) = x^{4} + y^{4} + 400 + 2 x^{2} y^{2}

Calculate

More Steps

Evaluate

x^{2} + 40 x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(1 + 40) x^{2}

Add the numbers

41 x^{2}

41 x^{2} + y^{2} = x^{4} + y^{4} + 400 + 2 x^{2} y^{2} - 40 y^{2}

Solution

More Steps

Evaluate

y^{2} + 40 y^{2}

Collect like terms by calculating the sum or difference of their coefficients

(1 + 40) y^{2}

Add the numbers

41 y^{2}

41 x^{2} + 41 y^{2} = x^{4} + y^{4} + 400 + 2 x^{2} y^{2}

Show Solution