Question

(x+6)^2 = (x+3)^2 + x^2​

Answer 1

Answer:

${(x + 6)}^{2} = {(x + 3)}^{2} + {x}^{2} \\ {x}^{2} + {6}^{2} = {x}^{2} + {3}^{2} + {x}^{2} \\ {x}^{2} + 36 = {x}^{4} + 9 \\ {x}^{2} - {x}^{4} = 9 - 36 \\ {\cancel - x}^{2} = \cancel- 27 \\ {x}^{2} = 27 \\ x = \sqrt{27 } \\\boxed{ x = 5.19}$

Answer 2

Answer:

X1 = -3 and X2 = 9

Step-by-step explanation:

$({x + 6})^{2} = ( {x + 3)}^{2} + {x}^{2}$

1ST STEP: EXPAND EQUATION BASE ON POWER/EXPONENT

${x}^{2} + 12x + 36 = {x}^{2} + 6x + 9+ {x}^{2}$

2ND STEP: ELIMINATE THE EQUATION ON THE LEFT SIDE BY SUBTRACTING ITS TERMS BUT IN NEGATIVE FORM.

NOTE: APPLY THE LAW OF MATHEMATICAL EQUATIONS, " WHAT YOU ADDED OR SUBTRACTED IN ON ONE SIDE OF THE EQUATION WILL BE COPIED ON THE OTHER SIDE OF THE EQUATION"

${x}^{2} + 12x + 36 - {x}^{2} - 12x - 36 = {x}^{2} + 6x + 9+ {x}^{2} - {x}^{2} - 12x - 36$

3RD STEP: COMBINE SIMILAR TERMS ON BOTH SIDES.

$0 = {x}^{2} + 6x - 12x + 9 - 36$

$0 = {x}^{2} - 6x - 27$

4TH STEP: FACTOR THE EQUATION

0= (x + 3) (x - 9)

5TH STEP: EQUATE BOTH FACTORS TO ZERO

x + 3 = 0

X1 = - 3

x - 9 = 0

X2 = 9