✏️QUADRATIC
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[tex] \large \bold{\blue{PROBLEM:}} [/tex] find the solution of the following quadratic equation x squared minus 4x + 4 = 0.
- [tex] x^2 - 4x + 4 = 0 [/tex]
[tex] \large \bold{\blue{SOLUTION:}} [/tex] The quadratic equation is already in standard form. Find the values of a, b, and c.
- [tex] \boxed{ax^2 + bx + c = 0} [/tex]
- [tex] a = 1, \: b = \text-4, \: c = 4 [/tex]
» Substitute the values to the quadratic formula to determine solutions.
- [tex] \boxed{x = \frac{\text-b \pm \sqrt{b^2 - 4ac}}{2a}} [/tex]
- [tex] x = \frac{\text-(\text-4) \pm \sqrt{(\text-4)^2 - 4(1)(4)}}{2(1)} \\ [/tex]
- [tex] x = \frac{\text-(\text-4) \pm \sqrt{16 - 4(1)(4)}}{2(1)} \\ [/tex]
- [tex] x = \frac{4 \pm \sqrt{16 - 16}}{2} \\ [/tex]
- [tex] x = \frac{4 \pm \sqrt{0}}{2} \\ [/tex]
» Since the discriminant (b² - 4ac) is equal to zero, then there will be one solution for this equation.
- [tex] x = \frac{4}{2} \\ [/tex]
[tex] \large \therefore \underline{\boxed{\tt \purple{x = 2}}} [/tex]
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