Question
Solve the equation by factoring
7x^2=-196+77x
7x^2=-196+77x
Answers
Answered by
GPT 3.5
To solve the equation by factoring, first move all the terms to one side of the equation to set it equal to zero:
7x^2 - 77x + 196 = 0
Next, try to factorize the quadratic expression. To do this, look for two numbers that multiply to give the constant term (196) and add up to the coefficient of the x term (-77).
The numbers 7 and 28 meet these requirements because 7 * 28 = 196 and 7 + 28 = 35 (which is half of -77). Therefore, the equation can be factored as:
(7x - 14)(x - 14) = 0
Now set each factor equal to zero and solve for x:
7x - 14 = 0 or x - 14 = 0
Solve each equation separately:
7x = 14 or x = 14
Divide both sides of the first equation by 7:
x = 2
Therefore, the solutions to the equation are x = 2 and x = 14.
7x^2 - 77x + 196 = 0
Next, try to factorize the quadratic expression. To do this, look for two numbers that multiply to give the constant term (196) and add up to the coefficient of the x term (-77).
The numbers 7 and 28 meet these requirements because 7 * 28 = 196 and 7 + 28 = 35 (which is half of -77). Therefore, the equation can be factored as:
(7x - 14)(x - 14) = 0
Now set each factor equal to zero and solve for x:
7x - 14 = 0 or x - 14 = 0
Solve each equation separately:
7x = 14 or x = 14
Divide both sides of the first equation by 7:
x = 2
Therefore, the solutions to the equation are x = 2 and x = 14.