3-10x(6-5x)=

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Solution for 3-10x(6-5x)= equation:


Simplifying
3 + -10x(6 + -5x) = 0
3 + (6 * -10x + -5x * -10x) = 0
3 + (-60x + 50x2) = 0

Solving
3 + -60x + 50x2 = 0

Solving for variable 'x'.

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

Divide each side by '50'.
0.06 + -1.2x + x2 = 0.0

Move the constant term to the right:

Add '-0.06' to each side of the equation.
0.06 + -1.2x + -0.06 + x2 = 0.0 + -0.06

Reorder the terms:
0.06 + -0.06 + -1.2x + x2 = 0.0 + -0.06

Combine like terms: 0.06 + -0.06 = 0.00
0.00 + -1.2x + x2 = 0.0 + -0.06
-1.2x + x2 = 0.0 + -0.06

Combine like terms: 0.0 + -0.06 = -0.06
-1.2x + x2 = -0.06

The x term is -1.2x.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2x + 0.36 + x2 = -0.06 + 0.36

Reorder the terms:
0.36 + -1.2x + x2 = -0.06 + 0.36

Combine like terms: -0.06 + 0.36 = 0.3
0.36 + -1.2x + x2 = 0.3

Factor a perfect square on the left side:
(x + -0.6)(x + -0.6) = 0.3

Calculate the square root of the right side: 0.547722558

Break this problem into two subproblems by setting 
(x + -0.6) equal to 0.547722558 and -0.547722558.

Subproblem 1

x + -0.6 = 0.547722558 Simplifying x + -0.6 = 0.547722558 Reorder the terms: -0.6 + x = 0.547722558 Solving -0.6 + x = 0.547722558 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 0.547722558 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 0.547722558 + 0.6 x = 0.547722558 + 0.6 Combine like terms: 0.547722558 + 0.6 = 1.147722558 x = 1.147722558 Simplifying x = 1.147722558

Subproblem 2

x + -0.6 = -0.547722558 Simplifying x + -0.6 = -0.547722558 Reorder the terms: -0.6 + x = -0.547722558 Solving -0.6 + x = -0.547722558 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -0.547722558 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -0.547722558 + 0.6 x = -0.547722558 + 0.6 Combine like terms: -0.547722558 + 0.6 = 0.052277442 x = 0.052277442 Simplifying x = 0.052277442

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.147722558, 0.052277442}

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