(4x)-(1.2x^2-11x-30)=

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Solution for (4x)-(1.2x^2-11x-30)= equation:


Simplifying
(4x) + -1(1.2x2 + -11x + -30) = 0

Reorder the terms:
(4x) + -1(-30 + -11x + 1.2x2) = 0
(4x) + (-30 * -1 + -11x * -1 + 1.2x2 * -1) = 0
(4x) + (30 + 11x + -1.2x2) = 0

Reorder the terms:
30 + (4x) + 11x + -1.2x2 = 0

Combine like terms: (4x) + 11x = 15x
30 + 15x + -1.2x2 = 0

Solving
30 + 15x + -1.2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1.2 the coefficient of the squared term: 

Divide each side by '-1.2'.
-25 + -12.5x + x2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -12.5x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + -12.5x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -12.5x + x2 = 0 + 25
-12.5x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
-12.5x + x2 = 25

The x term is -12.5x.  Take half its coefficient (-6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
-12.5x + 39.0625 + x2 = 25 + 39.0625

Reorder the terms:
39.0625 + -12.5x + x2 = 25 + 39.0625

Combine like terms: 25 + 39.0625 = 64.0625
39.0625 + -12.5x + x2 = 64.0625

Factor a perfect square on the left side:
(x + -6.25)(x + -6.25) = 64.0625

Calculate the square root of the right side: 8.003905297

Break this problem into two subproblems by setting 
(x + -6.25) equal to 8.003905297 and -8.003905297.

Subproblem 1

x + -6.25 = 8.003905297 Simplifying x + -6.25 = 8.003905297 Reorder the terms: -6.25 + x = 8.003905297 Solving -6.25 + x = 8.003905297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 8.003905297 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 8.003905297 + 6.25 x = 8.003905297 + 6.25 Combine like terms: 8.003905297 + 6.25 = 14.253905297 x = 14.253905297 Simplifying x = 14.253905297

Subproblem 2

x + -6.25 = -8.003905297 Simplifying x + -6.25 = -8.003905297 Reorder the terms: -6.25 + x = -8.003905297 Solving -6.25 + x = -8.003905297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -8.003905297 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -8.003905297 + 6.25 x = -8.003905297 + 6.25 Combine like terms: -8.003905297 + 6.25 = -1.753905297 x = -1.753905297 Simplifying x = -1.753905297

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.253905297, -1.753905297}

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