✏Quadratic Equation
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1.x(x + 5)=2
→Distribute
[tex]\purple{\boxed{\tt \: x(x+5)}}\tt \: = 2[/tex]
[tex]\purple{\boxed{\tt \: x² + 5x}}\tt \: = 2[/tex]
→Move terms to the left side
[tex]\tt \: x² + 5x = 2[/tex]
[tex]\tt \: x² + 5x - 2 = 0[/tex]
→Use the quadratic formula
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt \: x = \frac{ - b + \sqrt{b² - 4ac} }{2a} [/tex]
•Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.
[tex]\tt \: x² + 5x - 2 = 0[/tex]
[tex]\tt \: a = \purple{\boxed{\tt \: 1}}[/tex]
[tex]\tt \: b = \red{\boxed{\tt \: 5}}[/tex]
[tex]\tt \: c = \blue{\boxed{\tt \: - 2}}[/tex]
[tex]\tt \: x = \frac{ - 5 + \sqrt{5² - 4.1( - 2)} }{2.1} [/tex]
→Simplify
[tex]\tt \: x = \frac{ - 5 + \sqrt{33} }{2} [/tex]
→Separate the equations
- To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.
[tex]\tt \: x = \frac{ - 5 + \sqrt{33} }{2} [/tex]
[tex]\tt \: x = \frac{ - 5 - \sqrt{33} }{2} [/tex]
→Solve
- Rearrange and isolate the variable to find each solution
[tex]\tt \: x = \frac{ - 5 + \sqrt{33} }{2} [/tex]
[tex]\tt \: x = \frac{ - 5 - \sqrt{33} }{2} [/tex]
Answer:
- [tex]\blue{\boxed{\tt \: x =}}\tt \: \frac{ - 5 + \sqrt{33} }{2} [/tex]
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2.(s + 6)2 = 5
- [tex]\blue{\boxed{\tt \: (6, \: 4)}}[/tex]
- [tex]\pink{\boxed{\tt \: (6, \: - 3)}}[/tex]
- [tex]\red{\boxed{\tt \: (1, \: 3)}}[/tex]
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3.(x + )2 = 1 9
- [tex]\green{\boxed{\tt \: (1, \: 5)}}[/tex]
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