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Solve the equation [tex]4x^2 - 32x + 64 = 0[/tex]

[tex]x = \boxed{\phantom{x}}[/tex]

Sagot :

GinnyAnswer
To solve the quadratic equation [tex]\(4x^2 - 32x + 64 = 0\)[/tex], we can use the quadratic formula:

[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]

where [tex]\(a = 4\)[/tex], [tex]\(b = -32\)[/tex], and [tex]\(c = 64\)[/tex].

1. First, identify the coefficients:
- [tex]\(a = 4\)[/tex]
- [tex]\(b = -32\)[/tex]
- [tex]\(c = 64\)[/tex]

2. Calculate the discriminant [tex]\(\Delta\)[/tex]:
[tex]\[ \Delta = b^2 - 4ac \][/tex]
Substitute the values:
[tex]\[ \Delta = (-32)^2 - 4 \cdot 4 \cdot 64 \][/tex]
[tex]\[ \Delta = 1024 - 1024 \][/tex]
[tex]\[ \Delta = 0 \][/tex]

3. Since the discriminant is zero [tex]\(\Delta = 0\)[/tex], there is exactly one real root for the quadratic equation.

4. Use the quadratic formula to find the root:
[tex]\[ x = \frac{-b \pm \sqrt{0}}{2a} \][/tex]
[tex]\[ x = \frac{-(-32)}{2 \cdot 4} \][/tex]
[tex]\[ x = \frac{32}{8} \][/tex]
[tex]\[ x = 4 \][/tex]

Therefore, the solution to the equation [tex]\(4x^2 - 32x + 64 = 0\)[/tex] is:
[tex]\[ x = 4.0 \][/tex]

Since the discriminant is 0, the equation has only one unique real solution which is [tex]\(x = 4.0\)[/tex].
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