Solve 4a2 + 25 = –20a by factoring. Verify your solution
Solve and verify the following equation:
13x2 + 35x + 21 = –12x2 – 25x – 15
To solve the equation 4a^2 + 25 = -20a by factoring, we need to rewrite the equation in the form of a quadratic equation (ax^2 + bx + c = 0) and then factor it.
Step 1: Move all terms to one side of the equation to get it in the form of ax^2 + bx + c = 0:
4a^2 + 20a + 25 = 0
Step 2: Try to factor the expression. However, this quadratic equation cannot be factored easily using integers. Hence, we need to use the quadratic formula to solve for "a" if factoring is not possible.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / 2a
Here, a = 4, b = 20, and c = 25. Substituting these values into the quadratic formula, we get:
x = (-20 ± √(20^2 - 4 * 4 * 25)) / (2 * 4)
x = (-20 ± √(400 - 400)) / 8
x = (-20 ± √0) / 8
x = (-20 ± 0) / 8
Step 3: Simplify the expression further:
x = (-20 + 0) / 8 = -20/8 = -2.5
x = (-20 - 0) / 8 = -20/8 = -2.5
So, the solution to the equation 4a^2 + 25 = -20a is a = -2.5.
To verify the solution, let's substitute a = -2.5 back into the original equation and check if both sides are equal:
4(-2.5)^2 + 25 = -20(-2.5)
4(6.25) + 25 = 50
25 + 25 = 50
50 = 50
Since both sides of the equation are equal, we can conclude that the solution a = -2.5 is correct.
4a^2 + 25 = –20a
4a^2 + 20a + 25 = 0
(2a +5)^2 = 0
a = -5/2
13x^2 + 35x + 21 = –12x^2 – 25x – 15
25x^2 + 60x +36 = 0
(5a +6)^2 = 0
a = -6/5
You do the verifying.