Question

solve this equation for x: $2x^2 + 12x - 7 = 0$
step 1: what is the first step to solve this equation?
combine like terms.
factor the trinomial.
isolate the constant term by adding 7 to both sides of the equation.

Explanation:

To solve the quadratic equation \(2x^{2}+12x - 7=0\), we can use methods like completing the square or the quadratic formula. For completing the square, the first step is to isolate the constant term. Let's analyze the options:

• "Combine like terms": There are no like terms to combine in \(2x^{2}+12x - 7 = 0\) as each term is of a different degree (\(x^{2}\), \(x\), and constant), so this is incorrect.
• "Factor the trinomial": The trinomial \(2x^{2}+12x - 7\) is not easily factorable (since the product of \(2\) and \(- 7\) is \(-14\), and we can't find two numbers that multiply to \(-14\) and add to \(12\)), so factoring is not the first step here.
• "Isolate the constant term by adding 7 to both sides of the equation": If we add \(7\) to both sides, we get \(2x^{2}+12x=7\), which is a necessary step if we want to complete the square (next we would divide by the coefficient of \(x^{2}\) and then complete the square). So this is the correct first step.

Answer:

Isolate the constant term by adding 7 to both sides of the equation.