Question
Solve the equation. Round to the nearest hundredth.
7x^2 - 16x = 8
7x^2 - 16x = 8
Answers
Answered by
GPT 3.5
To solve the equation, we can rearrange it and set it equal to zero:
7x^2 - 16x - 8 = 0
Next, we can factor the quadratic equation by finding two numbers that add up to -16 and multiply to -56 (the product of 7 and -8). The two numbers are -14 and 4:
7x^2 - 14x + 4x - 8 = 0
7x(x - 2) + 4(x - 2) = 0
(7x + 4)(x - 2) = 0
Setting each factor equal to zero, we get:
7x + 4 = 0 or x - 2 = 0
Solving for x in each equation:
7x = -4 or x = 2
x = -4/7 or x = 2
To the nearest hundredth, x = -0.57 or x = 2.00.
7x^2 - 16x - 8 = 0
Next, we can factor the quadratic equation by finding two numbers that add up to -16 and multiply to -56 (the product of 7 and -8). The two numbers are -14 and 4:
7x^2 - 14x + 4x - 8 = 0
7x(x - 2) + 4(x - 2) = 0
(7x + 4)(x - 2) = 0
Setting each factor equal to zero, we get:
7x + 4 = 0 or x - 2 = 0
Solving for x in each equation:
7x = -4 or x = 2
x = -4/7 or x = 2
To the nearest hundredth, x = -0.57 or x = 2.00.