Question

Which of the following is the solution of One-fourth x + 5 = 7? x = 2 x = 6 x = 8 x = 12

Answer 1

Changes made to your input should not affect the solution:

(1): "x1" was replaced by "x^1". 3 more similar replacement(s).

Step by step solution :

Step 1 :

Equation at the end of step 1 :

x + ((((3•19x2) • x6) • x8) • x12)
Step 2 :

Step 3 :

Pulling out like terms :

3.1 Pull out like factors :

57x28 + x = x • (57x27 + 1)

Trying to factor as a Sum of Cubes :

3.2 Factoring: 57x27 + 1

Theory : A sum of two perfect cubes, a3 + b3 can be factored into :
(a+b) • (a2-ab+b2)
Proof : (a+b) • (a2-ab+b2) =
a3-a2b+ab2+ba2-b2a+b3 =
a3+(a2b-ba2)+(ab2-b2a)+b3=
a3+0+0+b3=
a3+b3

Check : 57 is not a cube !!


Final result :

x • (57x27 + 1)

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