What is the answer to (a+c)x+x^2=(x+a)^2 ?

The answer to (a+c)x+x^2=(x+a)^2 is x=(a^2)/(-a+c);\quad a\ne c

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(a+c)x+x^2=(x+a)^2

(a + c) x + x^{2} = (x + a)^{2}

x = \frac{a ^{2}}{- a + c}; a \neq = c

Solution steps

(a + c) x + x^{2} = (x + a)^{2}

Expand

(a + c) x + x^{2} : a x + c x + x^{2}

Expand

(x + a)^{2} : x^{2} + 2 a x + a^{2}

a x + c x + x^{2} = x^{2} + 2 a x + a^{2}

Subtract

x^{2} + 2 a x

from both sides

a x + c x + x^{2} - (x^{2} + 2 a x) = x^{2} + 2 a x + a^{2} - (x^{2} + 2 a x)

Simplify

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

Factor

- a x + c x : x (- a + c)

x (- a + c) = a^{2}

Divide both sides by

- a + c; a \neq = c

x = \frac{a ^{2}}{- a + c}; a \neq = c

lo g_{7} (5) = x

6 r + 16 (5 - r) = 70

\frac{1500 - d}{331.017} + \frac{d}{342.928} = 4.2

2 x (x + 3 y^{2} - 5) = 2 x^{2} + 6 x y^{2} - 2 x 5

x - \frac{x}{5} - \frac{x}{6} = 19

What is the answer to (a+c)x+x^2=(x+a)^2 ?
The answer to (a+c)x+x^2=(x+a)^2 is x=(a^2)/(-a+c);\quad a\ne c