(-3x^2+6x)-(7x^2+9x-3)=

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Solution for (-3x^2+6x)-(7x^2+9x-3)= equation:


Simplifying
(-3x2 + 6x) + -1(7x2 + 9x + -3) = 0

Reorder the terms:
(6x + -3x2) + -1(7x2 + 9x + -3) = 0

Remove parenthesis around (6x + -3x2)
6x + -3x2 + -1(7x2 + 9x + -3) = 0

Reorder the terms:
6x + -3x2 + -1(-3 + 9x + 7x2) = 0
6x + -3x2 + (-3 * -1 + 9x * -1 + 7x2 * -1) = 0
6x + -3x2 + (3 + -9x + -7x2) = 0

Reorder the terms:
3 + 6x + -9x + -3x2 + -7x2 = 0

Combine like terms: 6x + -9x = -3x
3 + -3x + -3x2 + -7x2 = 0

Combine like terms: -3x2 + -7x2 = -10x2
3 + -3x + -10x2 = 0

Solving
3 + -3x + -10x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
-0.3 + 0.3x + x2 = 0.0

Move the constant term to the right:

Add '0.3' to each side of the equation.
-0.3 + 0.3x + 0.3 + x2 = 0.0 + 0.3

Reorder the terms:
-0.3 + 0.3 + 0.3x + x2 = 0.0 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + 0.3x + x2 = 0.0 + 0.3
0.3x + x2 = 0.0 + 0.3

Combine like terms: 0.0 + 0.3 = 0.3
0.3x + x2 = 0.3

The x term is 0.3x.  Take half its coefficient (0.15).
Square it (0.0225) and add it to both sides.

Add '0.0225' to each side of the equation.
0.3x + 0.0225 + x2 = 0.3 + 0.0225

Reorder the terms:
0.0225 + 0.3x + x2 = 0.3 + 0.0225

Combine like terms: 0.3 + 0.0225 = 0.3225
0.0225 + 0.3x + x2 = 0.3225

Factor a perfect square on the left side:
(x + 0.15)(x + 0.15) = 0.3225

Calculate the square root of the right side: 0.567890835

Break this problem into two subproblems by setting 
(x + 0.15) equal to 0.567890835 and -0.567890835.

Subproblem 1

x + 0.15 = 0.567890835 Simplifying x + 0.15 = 0.567890835 Reorder the terms: 0.15 + x = 0.567890835 Solving 0.15 + x = 0.567890835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = 0.567890835 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = 0.567890835 + -0.15 x = 0.567890835 + -0.15 Combine like terms: 0.567890835 + -0.15 = 0.417890835 x = 0.417890835 Simplifying x = 0.417890835

Subproblem 2

x + 0.15 = -0.567890835 Simplifying x + 0.15 = -0.567890835 Reorder the terms: 0.15 + x = -0.567890835 Solving 0.15 + x = -0.567890835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = -0.567890835 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = -0.567890835 + -0.15 x = -0.567890835 + -0.15 Combine like terms: -0.567890835 + -0.15 = -0.717890835 x = -0.717890835 Simplifying x = -0.717890835

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.417890835, -0.717890835}

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