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Solusi - Memecahkan persamaan kuadrat dengan memfaktorkan

Exact form:

x_{1} = 3, x_{2} = - 3

x_1=3, x_2=-3

Decimal form:

x_{1} = 3, x_{2} = - 3

x_1=3, x_2=-3

Equation in factored form:

4 (x - 3) (x + 3) = 0

4(x-3)(x+3)=0

Lihat langkah

Penjelasan langkah demi langkah

1. Factor out the greatest common factor to get perfect squares

$4 x^{2} - 36 = 0$

Faktorkan dari istilah di sisi kiri:

$4 \cdot x^{2} - 4 \cdot 9 = 0$

$4 \cdot (x^{2} - 9) = 0$

2. Find the factors

$4 \cdot (x^{2} - 9) = 0$
Because both $x^{2}$ and $- 9$ are perfect squares, rewrite the equation using the difference of perfect squares formula:
$a^{2} - b^{2} = (a - b) (a + b)$ :
$4 (x + 3) (x - 3) = 0$

The factors of $4 x^{2} - 36 = 0$ are $4$ , $(x + 3)$ and $(x - 3)$ .

3. Find the roots of the quadratic equation

Find the roots of:
$4 x^{2} - 36 = 0$
using its factored form:
$4 (x + 3) (x - 3) = 0$

If
$4 (x + 3) (x - 3) = 0$
Then
$(x + 3) = 0$
and/or
$(x - 3) = 0$

Solve each factor for $x$ :

Factor 1:

2 tambahan langkah

$(x + 3) = 0$

Kurangi dari kedua ruas:

$(x + 3) - 3 = 0 - 3$

Sederhanakan hitungan:

$x = 0 - 3$

Sederhanakan hitungan:

$x = - 3$

Factor 2:

2 tambahan langkah

$(x - 3) = 0$

Tambahkan ke kedua sisi:

$(x - 3) + 3 = 0 + 3$

Sederhanakan hitungan:

$x = 0 + 3$

Sederhanakan hitungan:

$x = 3$

4. Graph

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[TRANSLATED] In their most basic function, quadratic equations define shapes like circles, ellipses and parabolas. These shapes can, in turn, be used to predict the curve of an object in motion, such as a ball kicked by a football player or a shot fired out of a cannon.
When it comes to an object’s movement through space, what better place to start than space itself, with the revolution of planets around the sun in our solar system? The quadratic equation was used to establish that planets’ orbits are elliptical, not circular. Determining the path and speed an object travels through space is possible even after it has come to a stop: the quadratic equation can calculate how fast a vehicle was moving when it crashed. With information like this, the automotive industry can design brakes to prevent collisions in the future. Many industries use the quadratic equation to predict and thus improve their products’ lifespan and safety.

Istilah dan topik

Lösen von quadratischen Gleichungen durch Ausklammern

Solusi - Memecahkan persamaan kuadrat dengan memfaktorkan

Penjelasan langkah demi langkah

1. Factor out the greatest common factor to get perfect squares

2. Find the factors

3. Find the roots of the quadratic equation

4. Graph

Alasan mempelajari materi ini

Istilah dan topik

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