3x(-3x+4)=-10

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Solution for 3x(-3x+4)=-10 equation:


Simplifying
3x(-3x + 4) = -10

Reorder the terms:
3x(4 + -3x) = -10
(4 * 3x + -3x * 3x) = -10
(12x + -9x2) = -10

Solving
12x + -9x2 = -10

Solving for variable 'x'.

Reorder the terms:
10 + 12x + -9x2 = -10 + 10

Combine like terms: -10 + 10 = 0
10 + 12x + -9x2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
-1.111111111 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '1.111111111' to each side of the equation.
-1.111111111 + -1.333333333x + 1.111111111 + x2 = 0 + 1.111111111

Reorder the terms:
-1.111111111 + 1.111111111 + -1.333333333x + x2 = 0 + 1.111111111

Combine like terms: -1.111111111 + 1.111111111 = 0.000000000
0.000000000 + -1.333333333x + x2 = 0 + 1.111111111
-1.333333333x + x2 = 0 + 1.111111111

Combine like terms: 0 + 1.111111111 = 1.111111111
-1.333333333x + x2 = 1.111111111

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = 1.111111111 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 1.111111111 + 0.4444444442

Combine like terms: 1.111111111 + 0.4444444442 = 1.5555555552
0.4444444442 + -1.333333333x + x2 = 1.5555555552

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 1.5555555552

Calculate the square root of the right side: 1.247219129

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 1.247219129 and -1.247219129.

Subproblem 1

x + -0.6666666665 = 1.247219129 Simplifying x + -0.6666666665 = 1.247219129 Reorder the terms: -0.6666666665 + x = 1.247219129 Solving -0.6666666665 + x = 1.247219129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 1.247219129 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 1.247219129 + 0.6666666665 x = 1.247219129 + 0.6666666665 Combine like terms: 1.247219129 + 0.6666666665 = 1.9138857955 x = 1.9138857955 Simplifying x = 1.9138857955

Subproblem 2

x + -0.6666666665 = -1.247219129 Simplifying x + -0.6666666665 = -1.247219129 Reorder the terms: -0.6666666665 + x = -1.247219129 Solving -0.6666666665 + x = -1.247219129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -1.247219129 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -1.247219129 + 0.6666666665 x = -1.247219129 + 0.6666666665 Combine like terms: -1.247219129 + 0.6666666665 = -0.5805524625 x = -0.5805524625 Simplifying x = -0.5805524625

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.9138857955, -0.5805524625}

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