A. Write The Equation 15 – 4k = -3k2in Standard Form.​

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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A. Write The Equation 15 – 4k = -3k2in Standard Form.​

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