Question

(x-4) square+25=169 solve this equation​

Answer 1

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                     x^2-(25/169)=0 

Step by step solution :STEP1: 25 Simplify ——— 169 Equation at the end of step1: 25 (x2) - ——— = 0 169 STEP 2 :Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  169  as the denominator :

x2 x2 • 169 x2 = —— = ———————— 1 169

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Answer 2

• Expand the square

${(x - 4)}^{2} + 25 = 169 \\ (x - 4)(x - 4) + 25 = 169$

• Distribute

$(x - 4)( x - 4) + 25 = 169 \\ x(x - 4) - 4(x - 4) + 25 = 169$

• Distribute

$x(x - 4) - 4(x - 4) + 25 = 169 \\ {x}^{2} - 4x - 4x + 16 + 25 = 169$

• Distribute

${x}^{2} - 4x - 4(x - 4) + 25 = 169 \\ {x}^{2} - 4x - 4x + 16 + 25 = 169$

• Combine like terms

${x}^{2} - 4x - 4x + 16 + 25 = 169 \\ {x}^{2} - 8x + 16 + 25 = 169$

• Add the numbers

${x}^{2} - 8x + 16 + 25 = 169 \\ {x}^{2} - 8x + 41 = 19$

• Move terms to the left side

${x}^{2} - 8x + 41 = 169 \\ {x}^{2} - 8x + 41 - 169 = 0$

• Subtract the numbers

${x}^{2} - 8x + 41 - 169 = 0 \\ {x}^{2} - 8x - 128 = 0$

• Use the sum-product pattern
• Identify a, b and c in your equation and then find two numbers that when multiplied together equal c, and when added together equal b.

x² - 8x - 128 = 0

• Factor
• Write your equation in factored form

$( x - 16)(x - 8) = 0$

• Create two separate equations
• Set each factor equal to zero

$x - 16 = 0 \\ x + 8 = 0$

• Solve
• Rearrange and isolate the variable to find each solution

$x = 16 \\ x = - 8$

Solution

$x = 16 \\ x = - 8$