Answer:
x = 3 and x = -7
Step-by-step explanation:
Solving :
⇒ x² + 4x - 21 = 0
⇒ x² + 7x - 3x - 21 = 0
⇒ x(x + 7) - 3(x + 7) = 0
⇒ (x - 3)(x + 7) = 0
⇒ x = 3 and x = -7
Answer:
[tex]x=3,\:x=-7[/tex]
Key:
• When doing a quadratic equation, one thing you must always know going into the equation is that you will have more than one answer.
Step-by-step explanation:
[tex]x^2+4x-21=0\\For\:\rightarrow\quad a=1,\:b=4,\:c=-21\\x_{1,\:2}=\frac{-4\pm \sqrt{4^2-4\cdot \:1\cdot \left(-21\right)}}{2\cdot \:1}\\\sqrt{4^2-4\cdot \:1\cdot \left(-21\right)}\\=\sqrt{4^2+4\cdot \:1\cdot \:21}\\=\sqrt{4^2+84}\\=\sqrt{16+84}\\=\sqrt{100}\\=\sqrt{10^2}\\=10\\x_{1,\:2}=\frac{-4\pm \:10}{2\cdot \:1}\\x_1=\frac{-4+10}{2\cdot \:1},\:x_2=\frac{-4-10}{2\cdot \:1}[/tex]
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Optional: Solve for x₁ and x₂
(x₁)
[tex]\frac{-4+10}{2\cdot \:1}\\=\frac{6}{2\cdot \:1}\\=\frac{6}{2}\\=3[/tex]
(x₂)
[tex]\frac{-4-10}{2\cdot \:1}\\=\frac{-14}{2\cdot \:1}\\=\frac{-14}{2}\\=-\frac{14}{2}\\=-7[/tex]
