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How do you solve #(4x + 3)^2 = 6#?

Answer 1

Kennedy Adams

Take the square root then solve two linear equations.

Since we have a squared term, lets begin by taking the square root of both sides, so that we have:

#4x+3 = +-sqrt(6)#

Let's subtract 3 on both sides:

#4x = +-sqrt(6) - 3#

Then divide by 4:

#x = (+-sqrt(6)-3)/4#

So we have two solutions:

#x = (sqrt(6)-3)/4#

#x = (-sqrt(6)-3)/4#

Including the #+-# is important, or else we would have missed one of the solutions.

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Answer 2

Abigail Allen

To solve the equation (4x + 3)^2 = 6, follow these steps:

Expand the square: 16x^2 + 24x + 9 = 6.
Subtract 6 from both sides: 16x^2 + 24x + 3 = 0.
This quadratic equation does not factor easily, so you can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).
Identify a, b, and c: a = 16, b = 24, c = 3.
Substitute the values into the quadratic formula and solve for x.

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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.