Solve r^2-4r-5=0 - ScanMath

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

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

Evaluate

r^{2} - 4 r - 5 = 0

Factor the expression

More Steps

Evaluate

r^{2} - 4 r - 5

Rewrite the expression

r^{2} + (1 - 5) r - 5

Calculate

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

Rewrite the expression

r \times r + r - 5 r - 5

Factor out r from the expression

r (r + 1) - 5 r - 5

Factor out - 5 from the expression

r (r + 1) - 5 (r + 1)

Factor out r + 1 from the expression

(r - 5) (r + 1)

(r - 5) (r + 1) = 0

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

r - 5 = 0 r + 1 = 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 + 1 = 0

Solve the equation for r

More Steps

Evaluate

r + 1 = 0

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

r = 0 - 1

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

r = - 1

r = 5 r = - 1

Solution

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

Show Solution

26 x^{2} + 26 y^{2} = x^{4} + y^{4} + 25 + 2 x^{2} y^{2}

Evaluate

r^{2} - 4 r - 5 = 0

Rewrite the expression

r^{2} - 4 r = 5

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

x^{2} + y^{2} - 4 r = 5

Simplify the expression

- 4 r = - x^{2} - y^{2} + 5

Square both sides of the equation

(- 4 r)^{2} = (- x^{2} - y^{2} + 5)^{2}

Evaluate

16 r^{2} = (- x^{2} - y^{2} + 5)^{2}

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

16 (x^{2} + y^{2}) = (- x^{2} - y^{2} + 5)^{2}

Calculate

16 x^{2} + 16 y^{2} = x^{4} + y^{4} + 25 + 2 x^{2} y^{2} - 10 x^{2} - 10 y^{2}

Move the expression to the left side

16 x^{2} + 16 y^{2} - (- 10 x^{2} - 10 y^{2}) = x^{4} + y^{4} + 25 + 2 x^{2} y^{2}

Calculate

More Steps

Evaluate

16 x^{2} + 10 x^{2}

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

(16 + 10) x^{2}

Add the numbers

26 x^{2}

26 x^{2} + 16 y^{2} = x^{4} + y^{4} + 25 + 2 x^{2} y^{2} - 10 y^{2}

Solution

More Steps

Evaluate

16 y^{2} + 10 y^{2}

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

(16 + 10) y^{2}

Add the numbers

26 y^{2}

26 x^{2} + 26 y^{2} = x^{4} + y^{4} + 25 + 2 x^{2} y^{2}

Show Solution