4x*(7x-6)=9*9

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Solution for 4x*(7x-6)=9*9 equation:


Simplifying
4x(7x + -6) = 9 * 9

Reorder the terms:
4x(-6 + 7x) = 9 * 9
(-6 * 4x + 7x * 4x) = 9 * 9
(-24x + 28x2) = 9 * 9

Multiply 9 * 9
-24x + 28x2 = 81

Solving
-24x + 28x2 = 81

Solving for variable 'x'.

Reorder the terms:
-81 + -24x + 28x2 = 81 + -81

Combine like terms: 81 + -81 = 0
-81 + -24x + 28x2 = 0

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

Divide each side by '28'.
-2.892857143 + -0.8571428571x + x2 = 0

Move the constant term to the right:

Add '2.892857143' to each side of the equation.
-2.892857143 + -0.8571428571x + 2.892857143 + x2 = 0 + 2.892857143

Reorder the terms:
-2.892857143 + 2.892857143 + -0.8571428571x + x2 = 0 + 2.892857143

Combine like terms: -2.892857143 + 2.892857143 = 0.000000000
0.000000000 + -0.8571428571x + x2 = 0 + 2.892857143
-0.8571428571x + x2 = 0 + 2.892857143

Combine like terms: 0 + 2.892857143 = 2.892857143
-0.8571428571x + x2 = 2.892857143

The x term is -0.8571428571x.  Take half its coefficient (-0.4285714286).
Square it (0.1836734694) and add it to both sides.

Add '0.1836734694' to each side of the equation.
-0.8571428571x + 0.1836734694 + x2 = 2.892857143 + 0.1836734694

Reorder the terms:
0.1836734694 + -0.8571428571x + x2 = 2.892857143 + 0.1836734694

Combine like terms: 2.892857143 + 0.1836734694 = 3.0765306124
0.1836734694 + -0.8571428571x + x2 = 3.0765306124

Factor a perfect square on the left side:
(x + -0.4285714286)(x + -0.4285714286) = 3.0765306124

Calculate the square root of the right side: 1.754004165

Break this problem into two subproblems by setting 
(x + -0.4285714286) equal to 1.754004165 and -1.754004165.

Subproblem 1

x + -0.4285714286 = 1.754004165 Simplifying x + -0.4285714286 = 1.754004165 Reorder the terms: -0.4285714286 + x = 1.754004165 Solving -0.4285714286 + x = 1.754004165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = 1.754004165 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = 1.754004165 + 0.4285714286 x = 1.754004165 + 0.4285714286 Combine like terms: 1.754004165 + 0.4285714286 = 2.1825755936 x = 2.1825755936 Simplifying x = 2.1825755936

Subproblem 2

x + -0.4285714286 = -1.754004165 Simplifying x + -0.4285714286 = -1.754004165 Reorder the terms: -0.4285714286 + x = -1.754004165 Solving -0.4285714286 + x = -1.754004165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = -1.754004165 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = -1.754004165 + 0.4285714286 x = -1.754004165 + 0.4285714286 Combine like terms: -1.754004165 + 0.4285714286 = -1.3254327364 x = -1.3254327364 Simplifying x = -1.3254327364

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.1825755936, -1.3254327364}

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