Question

Find using the Quadratic Formula x²-3x+27=6x+7

Answer 1

To solve the quadratic equation x²-3x+27=6x+7, rearrange it to x²-9x+20=0 and apply the quadratic formula. The solutions are x=5 and x=4.

Step-by-step explanation:

To solve the given quadratic equation x²-3x+27=6x+7 using the quadratic formula, we first need to rearrange the equation into the standard form ax²+bx+c = 0. Combining like terms, we get x²-9x+20 = 0. Once we have the coefficients, we can apply the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a),

which for our equation is:

• 
  
• a = 1,
• 
  
• b = -9,
• 
  
• c = 20.

Plugging these into the formula, we get:

x = (-(-9) ± √((-9)² - 4(1)(20))) / (2(1)),

x = (9 ± √(81 - 80)) / 2,

x = (9 ± √1) / 2,

So, we have two potential solutions.

For the positive root:

x = (9 + 1) / 2 = 10 / 2 = 5,

For the negative root:

x = (9 - 1) / 2 = 8 / 2 = 4.

Therefore, the solutions for the equation are x = 5 and x = 4.