12 x square + 7 x y - 12 Y Square square / 3 X + 4 Y
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12x2-7x-12=0 Two solutions were found : x = -3/4 = -0.750
x = 4/3 = 1.333
Step by step solution :Step 1 :Equation at the end of step 1 : ((22•3x2) - 7x) - 12 = 0 Step 2 :Trying to factor by splitting the middle term
2.1 Factoring 12x2-7x-12
The first term is, 12x2 its coefficient is 12 .
The middle term is, -7x its coefficient is -7 .
The last term, "the constant", is -12
Step-1 : Multiply the coefficient of the first term by the constant 12 • -12 = -144
Step-2 : Find two factors of -144 whose sum equals the coefficient of the middle term, which is -7 .
-144 + 1 = -143 -72 + 2 = -70 -48 + 3 = -45 -36 + 4 = -32 -24 + 6 = -18 -18 + 8 = -10 -16 + 9 = -7 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -16 and 9
12x2 - 16x + 9x - 12
Step-4 : Add up the first 2 terms, pulling out like factors :
4x • (3x-4)
Add up the last 2 terms, pulling out common factors :
3 • (3x-4)
Step-5 : Add up the four terms of step 4 :
(4x+3) • (3x-4)
Which is the desired factorization
Equation at the end of step 2 : (3x - 4) • (4x + 3) = 0 Step 3 :Theory - Roots of a product :
3.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation :
3.2 Solve : 3x-4 = 0
Add 4 to both sides of the equation :
3x = 4
Divide both sides of the equation by 3:
x = 4/3 = 1.333
Solving a Single Variable Equation :
3.3 Solve : 4x+3 = 0
Subtract 3 from both sides of the equation :
4x = -3
Divide both sides of the equation by 4:
x = -3/4 = -0.750
Supplement : Solving Quadratic Equation DirectlySolving 12x2-7x-12 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula
x = 4/3 = 1.333
Step by step solution :Step 1 :Equation at the end of step 1 : ((22•3x2) - 7x) - 12 = 0 Step 2 :Trying to factor by splitting the middle term
2.1 Factoring 12x2-7x-12
The first term is, 12x2 its coefficient is 12 .
The middle term is, -7x its coefficient is -7 .
The last term, "the constant", is -12
Step-1 : Multiply the coefficient of the first term by the constant 12 • -12 = -144
Step-2 : Find two factors of -144 whose sum equals the coefficient of the middle term, which is -7 .
-144 + 1 = -143 -72 + 2 = -70 -48 + 3 = -45 -36 + 4 = -32 -24 + 6 = -18 -18 + 8 = -10 -16 + 9 = -7 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -16 and 9
12x2 - 16x + 9x - 12
Step-4 : Add up the first 2 terms, pulling out like factors :
4x • (3x-4)
Add up the last 2 terms, pulling out common factors :
3 • (3x-4)
Step-5 : Add up the four terms of step 4 :
(4x+3) • (3x-4)
Which is the desired factorization
Equation at the end of step 2 : (3x - 4) • (4x + 3) = 0 Step 3 :Theory - Roots of a product :
3.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation :
3.2 Solve : 3x-4 = 0
Add 4 to both sides of the equation :
3x = 4
Divide both sides of the equation by 3:
x = 4/3 = 1.333
Solving a Single Variable Equation :
3.3 Solve : 4x+3 = 0
Subtract 3 from both sides of the equation :
4x = -3
Divide both sides of the equation by 4:
x = -3/4 = -0.750
Supplement : Solving Quadratic Equation DirectlySolving 12x2-7x-12 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula
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Step-by-step explanation:
12 एक्स स्क्वायर प्लस 7 एक्स वाई माइनस 12 स्क्वायर बाय 3 एक्स प्लस 4 बाय
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