A. Write the equation 15 – 4k = -3k2in standard form.
✏️Equation
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A. Write the equation 15 – 4k = -3k2in standard form.
→Rearrange terms
- [tex]\purple{\boxed{\tt15 – 4k = – 3k²}}[/tex]
- [tex]\purple{\boxed{\tt – 4k + 15 = – 3k²}}[/tex]
→Move terms to the left side
- [tex]\tt \: 4k + 15 = – 3k²[/tex]
- [tex]\tt4k + 15 – – 3k² = 0[/tex]
→Rearrange terms
- [tex]\tt4k + 15 – – 3k² = 0[/tex]
- [tex]\green{\boxed{\tt3k² – 4k + 15 = 0}}[/tex]
→Use the quadratic formula
- [tex]\tt \: k = \green{\boxed{\tt \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]\green{\boxed{\tt3k² – 4k + 15 = 0}}[/tex]
- [tex]\red{\boxed{\tt \: a = 3}}[/tex]
- [tex]\red{\boxed{\tt \: b = – 4}}[/tex]
- [tex]\blue{\boxed{\ \: c = 15}}[/tex]
[tex]\tt \: k = \blue{\boxed{\tt \frac{ – ( – 4) + \sqrt{( – 4)² – 4.3.15} }{2.3} }}[/tex]
→Simplify
- Evaluate the exponent
- Multiply the numbers
- Subtract the numbers
- Multiply the numbers
[tex]\tt \: k = \frac{4 + \sqrt{ – 164} }{6} [/tex]
→No real solutions because the discriminant is negative
- The square root of a negative number is not a real number
[tex]\green{\boxed{\tt \: d = -164}}[/tex]
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