Question

What is x? x^2+(x+1)^2=145

Answer 1

Answer: " x = 8, -9 " .
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Step-by-step explanation:
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Given:
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x² + (x + 1)² = 145 ; Solve for "x" :
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Note: (x+1)² = (x+1) (x+1) = x² + 1x + 1x + 1 = x² + 2x + 1 ;
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→ x² + (x + 1)² = x² + x² + 2x + 1 ;

= 2x² + 2x + 1 ;
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2x² + 2x + 1 = 145 ;

Subtract "1" from each side:
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↔ 2x² + 2x + 1 - 1 = 145 - 1 ;

to get:
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→ 2x² + 2x = 144 ;
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Now, subtract "144" from EACH SIDE of the equation:
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→ 2x² + 2x - 144 = 144 - 144 ;
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to get:

→ 2x² + 2x - 144 = 0 ;

which is an equation written in "quadratic format" that is:

" ax² + bx + c = 0 ; (a≠ 0) " ;
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We have:
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→ 2x² + 2x - 144 = 0 ;
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Divide each side of the equation by "2" ; to simplify:

→ {2x² + 2x - 144} / 2 = 0 / 2 ;
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to get:
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→ x² + x - 72 = 0 ;
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The "left-hand side" of the equation can be factored:
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(x - 8) (x + 9) = 0 ;
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→ x = 8, -9 .
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Answer 2

We want to determine x from the equation
x² + (x+1)² = 145

Expand.
x² + x² + 2x + 1 = 145
2x² + 2x + 1 - 145 = 0
2x² + 2x - 144 = 0
x² + x - 72 = 0

Factorize.
(x - 8)(x + 9) = 0

Therefore
x = 8, or x = -9

Answer: x = 8 or x = -9