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Solusi - Memecahkan persamaan kuadrat dengan memfaktorkan

Exact form:

m_{1} = - 10, m_{2} = 9

m_1=-10, m_2=9

Decimal form:

m_{1} = - 10, m_{2} = 9

m_1=-10, m_2=9

Equation in factored form:

(m + 10) (m - 9) = 0

(m+10)(m-9)=0

Lihat langkah

Penjelasan langkah demi langkah

1. Find the coefficients

[TRANSLATED] To find the coefficients, use the standard form of a quadratic equation:
$a x^{2} + b x + c = 0$
$m^{2} + 1 m - 90 = 0$

Coefficient $a$ $= 1$
Coefficient $b$ $= 1$
Coefficient $c$ $= - 90$

2. Find two numbers whose product equals $a \cdot c$ and sum equals $b$

Find the factors whose product equals coefficient $a$ multiplied by coefficient $c$ :
coefficient $a$ ∙ coefficient $c$ = $1$ ∙ $- 90$ = $- 90$

List the factors of $- 90$ :
$1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90$

Because the product of coefficient $a$ and coefficient $c$ equals a negative number $(- 90)$ one factor needs to be positive and the other one negative.

Dans la liste des facteurs, trouvez une paire dont la somme est égale au coefficient $b$ .
Coefficient $b$ = $1$

Este par no funciona.

$1 \cdot - 90 = - 90$

$1 - 90 = - 89$

Este par no funciona.

$2 \cdot - 45 = - 90$

$2 - 45 = - 43$

Este par no funciona.

$3 \cdot - 30 = - 90$

$3 - 30 = - 27$

Este par no funciona.

$5 \cdot - 18 = - 90$

$5 - 18 = - 13$

Este par no funciona.

$6 \cdot - 15 = - 90$

$6 - 15 = - 9$

Este par no funciona.

$9 \cdot - 10 = - 90$

$9 - 10 = - 1$

Lo encontró - este par resuelve el problema:

$10 \cdot - 9 = - 90$

$10 - 9 = 1$

The product of $10$ and $- 9$ equals coefficient $a$ $(1)$ multiplied by coefficient $c$ $(- 90)$ and their sum equals coefficient $b$ $(1)$ .

3. Split the middle term of the equation

$m^{2} + 1 m - 90 = 0$
Réécrivez le terme du milieu en utilisant $10$ et $- 9$ :
$m^{2} + 10 m - 9 m - 90 = 0$

4. Factor by grouping

$m^{2} + 10 m - 9 m - 90 = 0$

Factoriza los primeros dos términos y los dos últimos por separado:

$(m^{2} + 10 m) + (- 9 m - 90) = 0$

Factoriza el primer término:

$m (m + 10) + (- 9 m - 90) = 0$

Factoriza el segundo término:

$m (m + 10) - 9 (m + 10) = 0$

Factoriza el factor común máximo de cada grupo:

$(m + 10) (m - 9) = 0$

The factors of $m^{2} + 1 m - 90 = 0$ are $(m + 10)$ and $(m - 9)$ .

5. Find the roots of the quadratic equation

If
$(m + 10)$ ∙ $(m - 9) = 0$
Then
$(m + 10) = 0$
and/or
$(m - 9) = 0$

Solve each factor for $m$ :

Factor 1:

2 tambahan langkah

$(m + 10) = 0$

Kurangi dari kedua ruas:

$(m + 10) - 10 = 0 - 10$

Sederhanakan hitungan:

$m = 0 - 10$

Sederhanakan hitungan:

$m = - 10$

Factor 2:

2 tambahan langkah

$(m - 9) = 0$

Tambahkan ke kedua sisi:

$(m - 9) + 9 = 0 + 9$

Sederhanakan hitungan:

$m = 0 + 9$

Sederhanakan hitungan:

$m = 9$

6. 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. Find the coefficients

2. Find two numbers whose product equals a·c and sum equals b

3. Split the middle term of the equation

4. Factor by grouping

5. Find the roots of the quadratic equation

6. Graph

Alasan mempelajari materi ini

Istilah dan topik

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2. Find two numbers whose product equals $a \cdot c$ and sum equals $b$