What are the solutions to the equation x=10(4.7-x)^2 ?

The solutions to the equation x=10(4.7-x)^2 are x=(95+3sqrt(21))/(20),x=(95-3sqrt(21))/(20)

Find the zeros of x=10(4.7-x)^2

The zeros of x=10(4.7-x)^2 are x=(95+3sqrt(21))/(20),x=(95-3sqrt(21))/(20)

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x = 10 (4.7 - x)^{2}

x = \frac{95 + 3 21}{20}, x = \frac{95 - 3 21}{20}

Decimal Notation

x = 5.43738 \dots, x = 4.06261 \dots

Solution steps

x = 10 (4.7 - x)^{2}

Expand

10 (4.7 - x)^{2} : 220.9 - 94 x + 10 x^{2}

x = 220.9 - 94 x + 10 x^{2}

Switch sides

220.9 - 94 x + 10 x^{2} = x

Move

x

to the left side

10 x^{2} - 95 x + 220.9 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 95 ) \pm ( - 95 ) ^{2} - 4 \cdot 10 \cdot 220.9}{2 \cdot 10}

(- 95)^{2} - 4 \cdot 10 \cdot 220.9 = 321

x_{1, 2} = \frac{- ( - 95 ) \pm 3 21}{2 \cdot 10}

Separate the solutions

x_{1} = \frac{- ( - 95 ) + 3 21}{2 \cdot 10}, x_{2} = \frac{- ( - 95 ) - 3 21}{2 \cdot 10}

x = \frac{- ( - 95 ) + 3 21}{2 \cdot 10} : \frac{95 + 3 21}{20}

x = \frac{- ( - 95 ) - 3 21}{2 \cdot 10} : \frac{95 - 3 21}{20}

The solutions to the quadratic equation are:

x = \frac{95 + 3 21}{20}, x = \frac{95 - 3 21}{20}

x, x^{2} + 4 x y + 16 x^{2} = 0

(3 x - 2)^{2} = 121

5 \frac{( x - 2 ) ^{2}}{4} = 5

2 m^{2} + 7 m - 30 = 0

x^{2} - 2.5 x + 1 = 0

What are the solutions to the equation x=10(4.7-x)^2 ?
The solutions to the equation x=10(4.7-x)^2 are x=(95+3sqrt(21))/(20),x=(95-3sqrt(21))/(20)
Find the zeros of x=10(4.7-x)^2
The zeros of x=10(4.7-x)^2 are x=(95+3sqrt(21))/(20),x=(95-3sqrt(21))/(20)