Question

Solve for × : ײ+7×+12=0

Answer 1

-4

Explanation:

To solve the equation ײ + 7× + 12 = 0, we can use the factoring method or the quadratic formula.

Method 1: Factoring

Step 1: Look for two numbers that multiply to give the constant term (12) and add up to give the coefficient of the middle term (7). In this case, the numbers are 3 and 4.

Step 2: Rewrite the middle term using the two numbers found in step 1.

ײ + 3× + 4× + 12 = 0

Step 3: Group the terms and factor by grouping:

(ײ + 3×) + (4× + 12) = 0

×(× + 3) + 4(× + 3) = 0

(× + 3)(× + 4) = 0

Step 4: Set each factor equal to zero and solve for ×:

× + 3 = 0 or × + 4 = 0

× = -3 or × = -4

Method 2: Quadratic Formula

The quadratic formula is used when factoring is not possible or convenient.

Step 1: Identify the values of a, b, and c from the equation ax² + bx + c = 0. In this case, a = 1, b = 7, and c = 12.

Step 2: Substitute the values into the quadratic formula:

× = (-b ± √(b² - 4ac)) / (2a)

× = (-(7) ± √((7)² - 4(1)(12))) / (2(1))

× = (-7 ± √(49 - 48)) / 2

× = (-7 ± √1) / 2

× = (-7 ± 1) / 2

× = -6 / 2 or × = -8 / 2

× = -3 or × = -4

Therefore, the solutions to the equation ײ + 7× + 12 = 0 are × = -3 and × = -4!

Answer 2

x = - 4 , x = - 3

Explanation:

given the quadratic equation

x² + 7x + 12

consider the factors of the constant term (+ 12) which sum to give the coefficient of the x- term (+ 7)

the factors are + 4 and + 3 , since

+ 4 × + 3 = + 12 and 4 + 3 = + 7

use these factors to split the x- term

x² + 4x + 3x + 12 = 0 ( factor the first/second and third/fourth terms )

x(x + 4) + 3(x + 4) = 0 ← factor out (x + 4) from each term

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

equate each factor to zero and solve for x

x + 4 = 0 ( subtract 4 from both sides )

x = - 4

x + 3 = 0 ( subtract 3 from both sides )

x = - 3

solutions are x = - 4 , x = - 3