Question

Solve for x. Round your answers to two decimal places.

2x^2 + 6x = 4

x = −0.56 and x = 3.56
x = 0.56 and x = −3.56
x = −0.40 and x = 2.90
x = 0.40 and x = −2.90

Answer 1

(b) x = 0.56 and x = -3.56

Explanation:

You want the solutions to the equation 2x² +6x = 4.

Solutions

If p and q are solutions to the equation, it can be factored as ...

(x -p)(x -q) = 0

Expanding this gives ...

x² -(p+q)x +pq = 0

This tells us the coefficient of x is the opposite of the sum of the solutions, and the constant term is their product.

Equation

The given equation in standard form is ...

2x² +6x -4 = 0

We notice that the leading coefficient is a factor of all of the terms, so we can rewrite this as ...

x² +3x -2 = 0

Comparing this to the above relation regarding solutions, we see the sum of the solutions must be -3, the opposite of the coefficient of x.

Only one answer choice has solutions with the sum of -3:

x = 0.56 and x = -3.56

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