How do you solve #4x^2 +4x = 15# using the quadratic formula?

Answer 1

#x = 3/2, 5/2#.

First Of All, Convert the Equation to It's General Form #ax^2 + bx + c = 0#.

Thus, we have

#color(white)(xxx)4x^2 + 4x = 15#
#rArr 4x^2 + 4x - 15 = 0# [Subtract #15# from both sides.]

Thus, when we compare the equation to the general form, we obtain

#a = 4, b = 4, c = -15#.

Let's locate the discriminant now.

#D = b^2 - 4ac = 4^2 - 4*4*(-15) = 16 + 240 = 256#
As #D gt 0#, we will get two roots which are real and distinct.

Now apply Sridhar Acharya's Rule, also known as the quadratic formula (or whatever name it may be in your country).

#alpha = (-b + sqrt(D))/(2a) = (-4 + sqrt(256))/(2 * 4) = (-4 + 16)/(8) = 3/2#
And #beta = (-b - sqrt(D))/(2a) = (-4 - sqrt(256))/(2 * 4) = (-4 - 16)/(8) = 5/2#
So, #x = 3/2, 5/2#

I hope this is useful.

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Answer 2

#3/2 " or" - 5/2 #

Set the expression's value to 0.

#4 x^2 + 4x - 15 = 0#

Here is the quadratic formula:

# x = (-b +- sqrt (b^2 -4 a c )) / (2a) #

In this instance, we replace:

# a = 4, b = 4, c = -15#

Thus, the quadratic formula is as follows:

# x = (-4 +- sqrt (4^2 -4 * 4 *(-15) )) / (2*4) #
# = (-4 +- sqrt (16 + 240 )) / (8) #
# = (-4 +- 16) / (8) #
# = 3/2 "or" - 5/2 #

We can factorize this problem as well (you have to guess here).

#4 x^2 + 4x - 15 = 0#
#(2x + 5 ) (2x - 3) = 0 #

Next, to obtain the same answers, set both parenthesis to zero:

#(2x + 5 ) = 0 " or " (2x - 3) = 0 #
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Answer 3

To solve the quadratic equation 4x^2 + 4x = 15 using the quadratic formula, where ax^2 + bx + c = 0:

  1. Identify the coefficients:

    • a = 4
    • b = 4
    • c = -15
  2. Apply the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

  3. Substitute the coefficients into the formula: x = (-(4) ± √((4)^2 - 4(4)(-15))) / (2(4))

  4. Calculate the discriminant: Discriminant = b^2 - 4ac Discriminant = (4)^2 - 4(4)(-15) = 16 + 240 = 256

  5. Substitute the discriminant into the formula: x = (-4 ± √256) / (8)

  6. Simplify and solve for x: x = (-4 ± 16) / 8

    For the positive root: x = (-4 + 16) / 8 = 12 / 8 = 3/2

    For the negative root: x = (-4 - 16) / 8 = -20 / 8 = -5/2

Therefore, the solutions for the equation 4x^2 + 4x = 15 are x = 3/2 and x = -5/2.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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