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(x-2)(x-3)+(x-4)(x-5)=10/3
? Related: Using Quadratic Formula
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(x-2)(x-3)+(x-4)(x-5)=10/3 Related: Using Quadratic Formula?
(x-2)(x-3)+(x-4)(x-5)=10/3,
(x²-3x-2x+6)+(x²-5x-4x+20)=10/3,
x²-5x+6+x²-9x+20=10/3,
2x²-14x+26=10/3,
6x²-42x+78=10,
6x²-42x+68=0,
2(3x²-21x+34)=0,
3x²-21x+34=0,
x=-b±√b²-4ac/2a,.
=-(-21)±√(-21)²-4(3)(34)/2(3),
=21±√441-408/6,
=21±√33/6
(x²-3x-2x+6)+(x²-5x-4x+20)=10/3,
x²-5x+6+x²-9x+20=10/3,
2x²-14x+26=10/3,
6x²-42x+78=10,
6x²-42x+68=0,
2(3x²-21x+34)=0,
3x²-21x+34=0,
x=-b±√b²-4ac/2a,.
=-(-21)±√(-21)²-4(3)(34)/2(3),
=21±√441-408/6,
=21±√33/6
Community Answer
(x-2)(x-3)+(x-4)(x-5)=10/3 Related: Using Quadratic Formula?
Using Quadratic Formula to Solve (x-2)(x-3) (x-4)(x-5)=10/3
When you are given an equation with a product of factors, the first step is to expand the equation by multiplying the factors. After that, you can simplify the equation to its standard form and use the quadratic formula to solve it. Here are the steps to solve the given equation:
Step 1: Expand the Equation
Use the FOIL method to expand the equation:
(x-2)(x-3) (x-4)(x-5) = 10/3
(x² - 5x + 6) (x² - 9x + 20) = 10/3
(x² - 5x + 6) (x² - 9x + 20) = 10/3
Step 2: Simplify the Equation
Multiply the terms in the equation and simplify it to the standard form:
x⁴ - 14x³ + 65x² - 116x + 60 = 10/3
Convert the equation to the standard form by moving the constant to the left side:
x⁴ - 14x³ + 65x² - 116x + 60 - 10/3 = 0
3x⁴ - 42x³ + 195x² - 348x + 170 - 10 = 0
3x⁴ - 42x³ + 195x² - 348x + 160 = 0
3x⁴ - 42x³ + 195x² - 348x + 170 - 10 = 0
3x⁴ - 42x³ + 195x² - 348x + 160 = 0
Step 3: Use the Quadratic Formula
Use the quadratic formula to solve for x:
x = (-b ± sqrt(b² - 4ac)) / 2a
Identify the values of a, b, and c:
- a = 3
- b = -42
- c = 195
Substitute the values into the formula:
x = (-(-42) ± sqrt((-42)² - 4(3)(195))) / 2(3)
x = (42 ± sqrt(42² - 4(3)(195))) / 6
x = (42 ± sqrt(42² - 4(3)(195))) / 6
Simplify the expression:
x = (42 ± sqrt(-2316)) / 6
x = (42 ± 2i√579) / 6
x = (42 ± 2i√579) / 6
Therefore, the solutions are:
- x = (42 + 2i√579) / 6 = 7 + (1/3)i√579
- x = (42 - 2i√579) / 6 = 7 - (1/3)i√579
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(x-2)(x-3)+(x-4)(x-5)=10/3 Related: Using Quadratic Formula?
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