Solve r^2-4r-6=0 - ScanMath

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

r_{1} = 2 - 10, r_{2} = 2 + 10

Alternative Form

r_{1} \approx - 1.162278, r_{2} \approx 5.162278

Evaluate

r^{2} - 4 r - 6 = 0

Substitute a= 1,b= - 4 and c= - 6 into the quadratic formula r = \frac{- b \pm b ^{2} - 4 a c}{2 a}

r = \frac{4 \pm ( - 4 ) ^{2} - 4 ( - 6 )}{2}

Simplify the expression

More Steps

Evaluate

(- 4)^{2} - 4 (- 6)

Multiply the numbers

More Steps

Evaluate

4 (- 6)

Multiplying or dividing an odd number of negative terms equals a negative

- 4 \times 6

Multiply the numbers

- 24

(- 4)^{2} - (- 24)

Rewrite the expression

4^{2} - (- 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

4^{2} + 24

Evaluate the power

16 + 24

Add the numbers

40

r = \frac{4 \pm 40}{2}

Simplify the radical expression

More Steps

Evaluate

40

Write the expression as a product where the root of one of the factors can be evaluated

4 \times 10

Write the number in exponential form with the base of 2

2^{2} \times 10

The root of a product is equal to the product of the roots of each factor

2^{2} \times 10

Reduce the index of the radical and exponent with 2

210

r = \frac{4 \pm 2 10}{2}

Separate the equation into 2 possible cases

r = \frac{4 + 2 10}{2} r = \frac{4 - 2 10}{2}

Simplify the expression

More Steps

Evaluate

r = \frac{4 + 2 10}{2}

Divide the terms

More Steps

Evaluate

\frac{4 + 2 10}{2}

Rewrite the expression

\frac{2 ( 2 + 10 )}{2}

Reduce the fraction

2 + 10

r = 2 + 10

r = 2 + 10 r = \frac{4 - 2 10}{2}

Simplify the expression

More Steps

Evaluate

r = \frac{4 - 2 10}{2}

Divide the terms

More Steps

Evaluate

\frac{4 - 2 10}{2}

Rewrite the expression

\frac{2 ( 2 - 10 )}{2}

Reduce the fraction

2 - 10

r = 2 - 10

r = 2 + 10 r = 2 - 10

Solution

r_{1} = 2 - 10, r_{2} = 2 + 10

Alternative Form

r_{1} \approx - 1.162278, r_{2} \approx 5.162278

Show Solution

Rewrite the equation

28 x^{2} + 28 y^{2} = x^{4} + y^{4} + 36 + 2 x^{2} y^{2}

Evaluate

r^{2} - 4 r - 6 = 0

Rewrite the expression

r^{2} - 4 r = 6

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

x^{2} + y^{2} - 4 r = 6

Simplify the expression

- 4 r = - x^{2} - y^{2} + 6

Square both sides of the equation

(- 4 r)^{2} = (- x^{2} - y^{2} + 6)^{2}

Evaluate

16 r^{2} = (- x^{2} - y^{2} + 6)^{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} + 6)^{2}

Calculate

16 x^{2} + 16 y^{2} = x^{4} + y^{4} + 36 + 2 x^{2} y^{2} - 12 x^{2} - 12 y^{2}

Move the expression to the left side

16 x^{2} + 16 y^{2} - (- 12 x^{2} - 12 y^{2}) = x^{4} + y^{4} + 36 + 2 x^{2} y^{2}

Calculate

More Steps

Evaluate

16 x^{2} + 12 x^{2}

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

(16 + 12) x^{2}

Add the numbers

28 x^{2}

28 x^{2} + 16 y^{2} = x^{4} + y^{4} + 36 + 2 x^{2} y^{2} - 12 y^{2}

Solution

More Steps

Evaluate

16 y^{2} + 12 y^{2}

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

(16 + 12) y^{2}

Add the numbers

28 y^{2}

28 x^{2} + 28 y^{2} = x^{4} + y^{4} + 36 + 2 x^{2} y^{2}

Show Solution

Solve the quadratic equation

Rewrite the equation

Graph