What are the solutions to the equation 15^2=20^2+x^2-2*20*x*0.75 ?

The solutions to the equation 15^2=20^2+x^2-2*20*x*0.75 are x=5(3+sqrt(2)),x=5(3-sqrt(2))

Find the zeros of 15^2=20^2+x^2-2*20*x*0.75

The zeros of 15^2=20^2+x^2-2*20*x*0.75 are x=5(3+sqrt(2)),x=5(3-sqrt(2))

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1 5^{2} = 2 0^{2} + x^{2} - 2 \cdot 20 \cdot x \cdot 0.75

x = 5 (3 + 2), x = 5 (3 - 2)

Decimal Notation

x = 22.07106 \dots, x = 7.92893 \dots

Solution steps

1 5^{2} = 2 0^{2} + x^{2} - 2 \cdot 20 x \cdot 0.75

Expand

1 5^{2} : 225

Expand

2 0^{2} + x^{2} - 2 \cdot 20 x \cdot 0.75 : 400 + x^{2} - 30 x

225 = 400 + x^{2} - 30 x

Switch sides

400 + x^{2} - 30 x = 225

Move

225

to the left side

x^{2} - 30 x + 175 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 30 ) \pm ( - 30 ) ^{2} - 4 \cdot 1 \cdot 175}{2 \cdot 1}

(- 30)^{2} - 4 \cdot 1 \cdot 175 = 102

x_{1, 2} = \frac{- ( - 30 ) \pm 10 2}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 30 ) + 10 2}{2 \cdot 1}, x_{2} = \frac{- ( - 30 ) - 10 2}{2 \cdot 1}

x = \frac{- ( - 30 ) + 10 2}{2 \cdot 1} : 5 (3 + 2)

x = \frac{- ( - 30 ) - 10 2}{2 \cdot 1} : 5 (3 - 2)

The solutions to the quadratic equation are:

x = 5 (3 + 2), x = 5 (3 - 2)

2 u^{2} + u - 1 = 0

s^{2} + 12 s + 400 = 0

x^{2} + 37 x = 0

- 0.5 a^{2} + 243 a - 3280.5 = 0

2 a - 4 x = x^{2} + a^{2} - 4

What are the solutions to the equation 15^2=20^2+x^2-2*20*x*0.75 ?
The solutions to the equation 15^2=20^2+x^2-2*20*x*0.75 are x=5(3+sqrt(2)),x=5(3-sqrt(2))
Find the zeros of 15^2=20^2+x^2-2*20*x*0.75
The zeros of 15^2=20^2+x^2-2*20*x*0.75 are x=5(3+sqrt(2)),x=5(3-sqrt(2))