.9x-.7(12-2)=-.4x(x-.6)

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Solution for .9x-.7(12-2)=-.4x(x-.6) equation:


Simplifying
0.9x + -0.7(12 + -2) = -0.4x(x + -0.6)

Combine like terms: 12 + -2 = 10
0.9x + -0.7(10) = -0.4x(x + -0.6)

Multiply -0.7 * 10
0.9x + -7 = -0.4x(x + -0.6)

Reorder the terms:
-7 + 0.9x = -0.4x(x + -0.6)

Reorder the terms:
-7 + 0.9x = -0.4x(-0.6 + x)
-7 + 0.9x = (-0.6 * -0.4x + x * -0.4x)
-7 + 0.9x = (0.24x + -0.4x2)

Solving
-7 + 0.9x = 0.24x + -0.4x2

Solving for variable 'x'.

Combine like terms: 0.9x + -0.24x = 0.66x
-7 + 0.66x + 0.4x2 = 0.24x + -0.4x2 + -0.24x + 0.4x2

Reorder the terms:
-7 + 0.66x + 0.4x2 = 0.24x + -0.24x + -0.4x2 + 0.4x2

Combine like terms: 0.24x + -0.24x = 0.00
-7 + 0.66x + 0.4x2 = 0.00 + -0.4x2 + 0.4x2
-7 + 0.66x + 0.4x2 = -0.4x2 + 0.4x2

Combine like terms: -0.4x2 + 0.4x2 = 0.0
-7 + 0.66x + 0.4x2 = 0.0

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

Divide each side by '0.4'.
-17.5 + 1.65x + x2 = 0

Move the constant term to the right:

Add '17.5' to each side of the equation.
-17.5 + 1.65x + 17.5 + x2 = 0 + 17.5

Reorder the terms:
-17.5 + 17.5 + 1.65x + x2 = 0 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + 1.65x + x2 = 0 + 17.5
1.65x + x2 = 0 + 17.5

Combine like terms: 0 + 17.5 = 17.5
1.65x + x2 = 17.5

The x term is 1.65x.  Take half its coefficient (0.825).
Square it (0.680625) and add it to both sides.

Add '0.680625' to each side of the equation.
1.65x + 0.680625 + x2 = 17.5 + 0.680625

Reorder the terms:
0.680625 + 1.65x + x2 = 17.5 + 0.680625

Combine like terms: 17.5 + 0.680625 = 18.180625
0.680625 + 1.65x + x2 = 18.180625

Factor a perfect square on the left side:
(x + 0.825)(x + 0.825) = 18.180625

Calculate the square root of the right side: 4.263874412

Break this problem into two subproblems by setting 
(x + 0.825) equal to 4.263874412 and -4.263874412.

Subproblem 1

x + 0.825 = 4.263874412 Simplifying x + 0.825 = 4.263874412 Reorder the terms: 0.825 + x = 4.263874412 Solving 0.825 + x = 4.263874412 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.825' to each side of the equation. 0.825 + -0.825 + x = 4.263874412 + -0.825 Combine like terms: 0.825 + -0.825 = 0.000 0.000 + x = 4.263874412 + -0.825 x = 4.263874412 + -0.825 Combine like terms: 4.263874412 + -0.825 = 3.438874412 x = 3.438874412 Simplifying x = 3.438874412

Subproblem 2

x + 0.825 = -4.263874412 Simplifying x + 0.825 = -4.263874412 Reorder the terms: 0.825 + x = -4.263874412 Solving 0.825 + x = -4.263874412 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.825' to each side of the equation. 0.825 + -0.825 + x = -4.263874412 + -0.825 Combine like terms: 0.825 + -0.825 = 0.000 0.000 + x = -4.263874412 + -0.825 x = -4.263874412 + -0.825 Combine like terms: -4.263874412 + -0.825 = -5.088874412 x = -5.088874412 Simplifying x = -5.088874412

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.438874412, -5.088874412}

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