What are the solutions to the equation 16=36+x^2-12x-1/2 ?

The solutions to the equation 16=36+x^2-12x-1/2 are x=(12+sqrt(66))/2 ,x=(12-sqrt(66))/2

Find the zeros of 16=36+x^2-12x-1/2

The zeros of 16=36+x^2-12x-1/2 are x=(12+sqrt(66))/2 ,x=(12-sqrt(66))/2

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16 = 36 + x^{2} - 12 x - \frac{1}{2}

x = \frac{12 + 66}{2}, x = \frac{12 - 66}{2}

Decimal

x = 10.06201 \dots, x = 1.93798 \dots

Solution steps

16 = 36 + x^{2} - 12 x - \frac{1}{2}

Multiply both sides by

2

32 = 72 + 2 x^{2} - 24 x - 1

32 = 2 x^{2} - 24 x + 71

Switch sides

2 x^{2} - 24 x + 71 = 32

Move

32

to the left side

2 x^{2} - 24 x + 39 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 24 ) \pm ( - 24 ) ^{2} - 4 \cdot 2 \cdot 39}{2 \cdot 2}

(- 24)^{2} - 4 \cdot 2 \cdot 39 = 266

x_{1, 2} = \frac{- ( - 24 ) \pm 2 66}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 24 ) + 2 66}{2 \cdot 2}, x_{2} = \frac{- ( - 24 ) - 2 66}{2 \cdot 2}

x = \frac{- ( - 24 ) + 2 66}{2 \cdot 2} : \frac{12 + 66}{2}

x = \frac{- ( - 24 ) - 2 66}{2 \cdot 2} : \frac{12 - 66}{2}

The solutions to the quadratic equation are:

x = \frac{12 + 66}{2}, x = \frac{12 - 66}{2}

2^{x} = 32

∣ 2 x - 3 ∣ = ∣ x + 4 ∣

3^{7}

5 x^{2} - 14 x + 9 \leq 0

\frac{x ^{2} y ^{8}}{x ^{- 6} y ^{- 4}}

What are the solutions to the equation 16=36+x^2-12x-1/2 ?
The solutions to the equation 16=36+x^2-12x-1/2 are x=(12+sqrt(66))/2 ,x=(12-sqrt(66))/2
Find the zeros of 16=36+x^2-12x-1/2
The zeros of 16=36+x^2-12x-1/2 are x=(12+sqrt(66))/2 ,x=(12-sqrt(66))/2