Solve equations with quadratic function (while showing work) a) 3x2+x−5=0 b) x2−5x−8=0 c) b2+3b−6=0 d) 2n2−3n−8=0

Step 1 a) 3x2+x−5=0 Decording to quadratic formula x=−b±b2−4ac2a [ax2+bx+c=0] =−1±12−4×3×−52×3=−1±1+606 =−1±616 x=−1+616 x=−1−616 Step 2 b) x2−5x−8=0 x=−(−5)±(−5)2−4×1×1×−82×1 =5±25+322 =5±572 x=5+572 or x=5−572 Step 3 c) b2+36−6=0 b=−3±32−4×1×−62×1 =−3±9+242 =−3±332 b=−3+332, b=−3−332 Step 4 d) 2n2−3n−8=0 n=−(−3)±−32−4×2×−82×2 =3±9+644 =3±734 n=3+734 or n=3−734

"Solve equations with quadratic function (while showing work)..." solved and explained

High School
Algebra
Algebra I
Quadratic function and equation

snijelihd

Answered question

2021-12-06

Solve equations with quadratic function (while showing work)
a)

3 x^{2} + x - 5 = 0

x^{2} - 5 x - 8 = 0

b^{2} + 3 b - 6 = 0

2 n^{2} - 3 n - 8 = 0

Answer & Explanation

Tamara Donohue

Beginner2021-12-07Added 11 answers

Step 1
a)

3 x^{2} + x - 5 = 0

Decording to quadratic formula

x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} [a x^{2} + b x + c = 0]

= \frac{- 1 \pm \sqrt{1^{2} - 4 \times 3 \times - 5}}{2 \times 3} = \frac{- 1 \pm \sqrt{1 + 60}}{6}

= \frac{- 1 \pm \sqrt{61}}{6}

x = \frac{- 1 + \sqrt{61}}{6}

x = \frac{- 1 - \sqrt{61}}{6}

Step 2
b)

x^{2} - 5 x - 8 = 0

x = \frac{- (- 5) \pm \sqrt{{(- 5)}^{2} - 4 \times 1 \times 1 \times - 8}}{2 \times 1}

= \frac{5 \pm \sqrt{25 + 32}}{2}

= \frac{5 \pm \sqrt{57}}{2}

x = \frac{5 + \sqrt{57}}{2}

x = \frac{5 - \sqrt{57}}{2}

Step 3
c)

b^{2} + 36 - 6 = 0

b = \frac{- 3 \pm \sqrt{3^{2} - 4 \times 1 \times - 6}}{2 \times 1}

= \frac{- 3 \pm \sqrt{9 + 24}}{2}

= \frac{- 3 \pm \sqrt{33}}{2}

b = \frac{- 3 + \sqrt{33}}{2}, b = \frac{- 3 - \sqrt{33}}{2}

Step 4
d)

2 n^{2} - 3 n - 8 = 0

n = \frac{- (- 3) \pm \sqrt{- 3^{2} - 4 \times 2 \times - 8}}{2 \times 2}

= \frac{3 \pm \sqrt{9 + 64}}{4}

= \frac{3 \pm \sqrt{73}}{4}

n = \frac{3 + \sqrt{73}}{4}

n = \frac{3 - \sqrt{73}}{4}

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