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Chapter 6: Problem 91

Explain how to solve a quadratic equation using the quadratic formula. Use the equation \(x^{2}+6 x+8=0\) in your explanation.

Short Answer

Expert verified
The roots of the quadratic equation \(x^{2} +6x +8=0\) are \(x = -2\) and \(x = -4\).

Step by step solution

01

Identify the coefficients

From the given quadratic equation \(x^{2} +6x +8=0\), identify the coefficients \(a, b, c\) which are \(a=1\), \(b=6\), \(c=8\).
02

Write down the quadratic formula

The quadratic formula is given by \(x = \frac{{-b \pm \sqrt{{b^{2}-4ac}}}}{{2a}}\), where \(a\) is the coefficient of the quadratic term \(x^{2}\), \(b\) is the coefficient of the linear term \(x\), and \(c\) is the constant term.
03

Substitute values into the quadratic formula

Substitute the values \(a=1\), \(b=6\), \(c=8\) into the quadratic formula. You will have \(x = \frac{{-6 \pm \sqrt{{6^{2}-4*1*8}}}}{{2*1}}\.
04

Simplify the expressions under and outside the square root

Simplify the expressions under the square root which leads to \(x = \frac{{-6 \pm \sqrt{{36-32}}}}{2}\), thus \(x = \frac{{-6 \pm \sqrt{4}}}{2}\).
05

Simplify further to find the values of x

Further simplification of the expression gives two solutions \(x = \frac{{-6 + 2}}{2} = -2\) and \(x = \frac{{-6 - 2}}{2} = -4\). Thus the roots of the quadratic equation are \(x = -2\) and \(x = -4\).

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I began the solution of \(5-3(x+2)>10 x\) by simplifying the left side, obtaining \(2 x+4>10 x\).

Solve the equations using the quadratic formula. \(x^{2}+2 x=4\)

Solve the quadratic equations by factoring. \(x^{2}-2 x-15=0\)

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(x^{2}-7 x-44\)

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(x^{2}+17 x+16\)
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