Solve using the Square Root Property 200x-x^2=40x+3375

$200 x - x^{2} = 40 x + 3375$

Set the equation equal to zero.

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Move all the expressions to the left side of the equation.

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Move $40 x$ to the left side of the equation by subtracting it from both sides.

$200 x - x^{2} - 40 x = 3375$

Move $3375$ to the left side of the equation by subtracting it from both sides.

$200 x - x^{2} - 40 x - 3375 = 0$

Subtract $40 x$ from $200 x$ .

$- x^{2} + 160 x - 3375 = 0$

Factor the left side of the equation.

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Factor by grouping.

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For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = - 1 \cdot - 3375 = 3375$ and whose sum is $b = 160$ .

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Factor $160$ out of $160 x$ .

$- x^{2} + 160 (x) - 3375$

Rewrite $160$ as $25$ plus $135$

$- x^{2} + (25 + 135) x - 3375$

Apply the distributive property.

$- x^{2} + 25 x + 135 x - 3375$

Factor out the greatest common factor from each group.

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Group the first two terms and the last two terms.

$(- x^{2} + 25 x) + 135 x - 3375$

Factor out the greatest common factor (GCF) from each group.

$x (- x + 25) - 135 (- x + 25)$

Factor the polynomial by factoring out the greatest common factor, $- x + 25$ .

$(- x + 25) (x - 135)$

Replace the left side with the factored expression.

$(- x + 25) (x - 135) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$- x + 25 = 0$

$x - 135 = 0$

Set the first factor equal to $0$ and solve.

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Set the first factor equal to $0$ .

$- x + 25 = 0$

Subtract $25$ from both sides of the equation.

$- x = - 25$

Multiply each term in $- x = - 25$ by $- 1$

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Multiply each term in $- x = - 25$ by $- 1$ .

$(- x) \cdot - 1 = (- 25) \cdot - 1$

Multiply $(- x) \cdot - 1$ .

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Multiply $- 1$ by $- 1$ .

$1 x = (- 25) \cdot - 1$

Multiply $x$ by $1$ .

$x = (- 25) \cdot - 1$

Multiply $- 25$ by $- 1$ .

$x = 25$

Set the next factor equal to $0$ and solve.

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Set the next factor equal to $0$ .

$x - 135 = 0$

Add $135$ to both sides of the equation.

$x = 135$

The final solution is all the values that make $(- x + 25) (x - 135) = 0$ true.

$x = 25, 135$

Solve using the Square Root Property 200x-x^2=40x+3375

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