What is the answer to solvefor x,(x-p)^2=(x-q)^2 ?

The answer to solvefor x,(x-p)^2=(x-q)^2 is x=(q+p)/2 ;\quad p\ne q

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solvefor x,(x-p)^2=(x-q)^2

solve for

x, (x - p)^{2} = (x - q)^{2}

x = \frac{q + p}{2}; p \neq = q

Solution steps

(x - p)^{2} = (x - q)^{2}

Expand

(x - p)^{2} : x^{2} - 2 x p + p^{2}

Expand

(x - q)^{2} : x^{2} - 2 x q + q^{2}

x^{2} - 2 x p + p^{2} = x^{2} - 2 x q + q^{2}

Move

p^{2}

to the right side

x^{2} - 2 x p = x^{2} - 2 x q + q^{2} - p^{2}

Subtract

x^{2} - 2 x q

from both sides

x^{2} - 2 x p - (x^{2} - 2 x q) = x^{2} - 2 x q + q^{2} - p^{2} - (x^{2} - 2 x q)

Simplify

- 2 x p + 2 x q = q^{2} - p^{2}

Factor

- 2 x p + 2 x q : 2 x (- p + q)

2 x (- p + q) = q^{2} - p^{2}

Divide both sides by

2 (- p + q); p \neq = q

x = \frac{q + p}{2}; p \neq = q

2 (5 + 4 x) = 30

2 \cdot x = 6.67

x, 14 x + 28 = 56 y + 42

x, 2 f + 3 f (1 - x) = 4 x - 1

x, 5 x + 2 y = - 29

What is the answer to solvefor x,(x-p)^2=(x-q)^2 ?
The answer to solvefor x,(x-p)^2=(x-q)^2 is x=(q+p)/2 ;\quad p\ne q