Identify the quadratic equation.

Mathematics

ScanSolve AI Answer

Answer

x=−2,x=−5x = -2, x = -5

Step-by-step solution

6 steps

  1. Identify the quadratic equation.

    The given equation is x2+7x+10=0x^2 + 7x + 10 = 0. To factorize this, we need to find two numbers that multiply to the constant term (10) and add up to the coefficient of the middle term (7).

  2. Find the two numbers.

    The two numbers that satisfy these conditions are 2 and 5, because 2×5=102 \times 5 = 10 and 2+5=72 + 5 = 7.

  3. Rewrite the middle term using these numbers.

    Rewrite 7x7x as 2x+5x2x + 5x:

    x2+2x+5x+10=0x^2 + 2x + 5x + 10 = 0

  4. Group the terms and factor out common factors.

    Group the first two terms and the last two terms:

    (x2+2x)+(5x+10)=0(x^2 + 2x) + (5x + 10) = 0

    Factor out xx from the first group and 5 from the second group:

    x(x+2)+5(x+2)=0x(x + 2) + 5(x + 2) = 0

  5. Factor out the common binomial.

    Notice that (x+2)(x + 2) is a common factor:

    (x+2)(x+5)=0(x + 2)(x + 5) = 0

  6. Set each factor to zero to solve for xx.

    For the product of two factors to be zero, at least one of the factors must be zero.

    x+2=0orx+5=0x + 2 = 0 \quad \text{or} \quad x + 5 = 0

    Solving for xx in each case:

    x=−2orx=−5x = -2 \quad \text{or} \quad x = -5

    The solutions for the equation are:

    x=−2,x=−5x = -2, x = -5
Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QIdentify the quadratic expression.QIdentify the coefficients of the quadratic equation.QIdentify the given quadratic equation and its roots.QWrite the quadratic equation.QForm the quadratic equation.
Browse by topic:Algebra
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.