(4.20x-5.80)(7.20x-9.20)=8.90x+10.3

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Solution for (4.20x-5.80)(7.20x-9.20)=8.90x+10.3 equation:


Simplifying
(4.20x + -5.80)(7.20x + -9.20) = 8.90x + 10.3

Reorder the terms:
(-5.80 + 4.20x)(7.20x + -9.20) = 8.90x + 10.3

Reorder the terms:
(-5.80 + 4.20x)(-9.20 + 7.20x) = 8.90x + 10.3

Multiply (-5.80 + 4.20x) * (-9.20 + 7.20x)
(-5.80(-9.20 + 7.20x) + 4.20x * (-9.20 + 7.20x)) = 8.90x + 10.3
((-9.20 * -5.80 + 7.20x * -5.80) + 4.20x * (-9.20 + 7.20x)) = 8.90x + 10.3
((53.36 + -41.76x) + 4.20x * (-9.20 + 7.20x)) = 8.90x + 10.3
(53.36 + -41.76x + (-9.20 * 4.20x + 7.20x * 4.20x)) = 8.90x + 10.3
(53.36 + -41.76x + (-38.64x + 30.24x2)) = 8.90x + 10.3

Combine like terms: -41.76x + -38.64x = -80.4x
(53.36 + -80.4x + 30.24x2) = 8.90x + 10.3

Reorder the terms:
53.36 + -80.4x + 30.24x2 = 10.3 + 8.90x

Solving
53.36 + -80.4x + 30.24x2 = 10.3 + 8.90x

Solving for variable 'x'.

Reorder the terms:
53.36 + -10.3 + -80.4x + -8.90x + 30.24x2 = 10.3 + 8.90x + -10.3 + -8.90x

Combine like terms: 53.36 + -10.3 = 43.06
43.06 + -80.4x + -8.90x + 30.24x2 = 10.3 + 8.90x + -10.3 + -8.90x

Combine like terms: -80.4x + -8.90x = -89.3x
43.06 + -89.3x + 30.24x2 = 10.3 + 8.90x + -10.3 + -8.90x

Reorder the terms:
43.06 + -89.3x + 30.24x2 = 10.3 + -10.3 + 8.90x + -8.90x

Combine like terms: 10.3 + -10.3 = 0.0
43.06 + -89.3x + 30.24x2 = 0.0 + 8.90x + -8.90x
43.06 + -89.3x + 30.24x2 = 8.90x + -8.90x

Combine like terms: 8.90x + -8.90x = 0.00
43.06 + -89.3x + 30.24x2 = 0.00

Begin completing the square.  Divide all terms by
30.24 the coefficient of the squared term: 

Divide each side by '30.24'.
1.423941799 + -2.953042328x + x2 = 0

Move the constant term to the right:

Add '-1.423941799' to each side of the equation.
1.423941799 + -2.953042328x + -1.423941799 + x2 = 0 + -1.423941799

Reorder the terms:
1.423941799 + -1.423941799 + -2.953042328x + x2 = 0 + -1.423941799

Combine like terms: 1.423941799 + -1.423941799 = 0.000000000
0.000000000 + -2.953042328x + x2 = 0 + -1.423941799
-2.953042328x + x2 = 0 + -1.423941799

Combine like terms: 0 + -1.423941799 = -1.423941799
-2.953042328x + x2 = -1.423941799

The x term is -2.953042328x.  Take half its coefficient (-1.476521164).
Square it (2.180114748) and add it to both sides.

Add '2.180114748' to each side of the equation.
-2.953042328x + 2.180114748 + x2 = -1.423941799 + 2.180114748

Reorder the terms:
2.180114748 + -2.953042328x + x2 = -1.423941799 + 2.180114748

Combine like terms: -1.423941799 + 2.180114748 = 0.756172949
2.180114748 + -2.953042328x + x2 = 0.756172949

Factor a perfect square on the left side:
(x + -1.476521164)(x + -1.476521164) = 0.756172949

Calculate the square root of the right side: 0.869582054

Break this problem into two subproblems by setting 
(x + -1.476521164) equal to 0.869582054 and -0.869582054.

Subproblem 1

x + -1.476521164 = 0.869582054 Simplifying x + -1.476521164 = 0.869582054 Reorder the terms: -1.476521164 + x = 0.869582054 Solving -1.476521164 + x = 0.869582054 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.476521164' to each side of the equation. -1.476521164 + 1.476521164 + x = 0.869582054 + 1.476521164 Combine like terms: -1.476521164 + 1.476521164 = 0.000000000 0.000000000 + x = 0.869582054 + 1.476521164 x = 0.869582054 + 1.476521164 Combine like terms: 0.869582054 + 1.476521164 = 2.346103218 x = 2.346103218 Simplifying x = 2.346103218

Subproblem 2

x + -1.476521164 = -0.869582054 Simplifying x + -1.476521164 = -0.869582054 Reorder the terms: -1.476521164 + x = -0.869582054 Solving -1.476521164 + x = -0.869582054 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.476521164' to each side of the equation. -1.476521164 + 1.476521164 + x = -0.869582054 + 1.476521164 Combine like terms: -1.476521164 + 1.476521164 = 0.000000000 0.000000000 + x = -0.869582054 + 1.476521164 x = -0.869582054 + 1.476521164 Combine like terms: -0.869582054 + 1.476521164 = 0.60693911 x = 0.60693911 Simplifying x = 0.60693911

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.346103218, 0.60693911}

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