(A)Write the equation in standard form and calculate its discriminant. (B)Solve the equation by using the quadratic formula. (C)After solving the equation, write it in factored form. 7x(x-2)+2(x+4)=3 Please help!!!!! :(
7x(x-2)+2(x+4)=3
7x^2-14x+2x+8-3=0
7x^2-12x+5=0
B just plug in your numbers in the QF to find the roots
C if your roots are p/7 and q, then it is (7x-p)(x-q)
Sure! I can help you with that.
(A) To write the equation in standard form, we need to expand and simplify the equation. Let's start by distributing terms:
7x(x-2) + 2(x+4) = 3
7x^2 - 14x + 2x + 8 = 3
Next, combine like terms:
7x^2 - 12x + 8 = 3
Now let's rearrange the equation to put it in standard form:
7x^2 - 12x + 8 - 3 = 0
7x^2 - 12x + 5 = 0
The equation is now in standard form, which is ax^2 + bx + c = 0. In this case, a = 7, b = -12, and c = 5.
To calculate the discriminant, we use the formula Δ = b^2 - 4ac. Plugging in the values, we have:
Δ = (-12)^2 - 4(7)(5) = 144 - 140 = 4
So the discriminant is 4.
(B) To solve the equation using the quadratic formula, we use the formula: x = (-b ± sqrt(Δ)) / (2a).
Plugging in the values from the standard form equation, we have:
x = (-(-12) ± sqrt(4)) / (2 * 7)
= (12 ± 2) / 14
Therefore, we have two solutions:
x = (12 + 2) / 14 = 14 / 14 = 1
x = (12 - 2) / 14 = 10 / 14 = 5/7
So the solutions to the equation are x = 1 and x = 5/7.
(C) After solving the equation, we can write it in factored form using the solutions we found:
Since x = 1 and x = 5/7 are solutions to the equation, we can write it as:
(x - 1)(x - 5/7) = 0
And there you have it! The equation written in factored form is (x - 1)(x - 5/7) = 0.