3x^2-28+2x^2-3x=360

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Solution for 3x^2-28+2x^2-3x=360 equation:


Simplifying
3x2 + -28 + 2x2 + -3x = 360

Reorder the terms:
-28 + -3x + 3x2 + 2x2 = 360

Combine like terms: 3x2 + 2x2 = 5x2
-28 + -3x + 5x2 = 360

Solving
-28 + -3x + 5x2 = 360

Solving for variable 'x'.

Reorder the terms:
-28 + -360 + -3x + 5x2 = 360 + -360

Combine like terms: -28 + -360 = -388
-388 + -3x + 5x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-388 + -3x + 5x2 = 0

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

Divide each side by '5'.
-77.6 + -0.6x + x2 = 0

Move the constant term to the right:

Add '77.6' to each side of the equation.
-77.6 + -0.6x + 77.6 + x2 = 0 + 77.6

Reorder the terms:
-77.6 + 77.6 + -0.6x + x2 = 0 + 77.6

Combine like terms: -77.6 + 77.6 = 0.0
0.0 + -0.6x + x2 = 0 + 77.6
-0.6x + x2 = 0 + 77.6

Combine like terms: 0 + 77.6 = 77.6
-0.6x + x2 = 77.6

The x term is -0.6x.  Take half its coefficient (-0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
-0.6x + 0.09 + x2 = 77.6 + 0.09

Reorder the terms:
0.09 + -0.6x + x2 = 77.6 + 0.09

Combine like terms: 77.6 + 0.09 = 77.69
0.09 + -0.6x + x2 = 77.69

Factor a perfect square on the left side:
(x + -0.3)(x + -0.3) = 77.69

Calculate the square root of the right side: 8.8141931

Break this problem into two subproblems by setting 
(x + -0.3) equal to 8.8141931 and -8.8141931.

Subproblem 1

x + -0.3 = 8.8141931 Simplifying x + -0.3 = 8.8141931 Reorder the terms: -0.3 + x = 8.8141931 Solving -0.3 + x = 8.8141931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 8.8141931 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 8.8141931 + 0.3 x = 8.8141931 + 0.3 Combine like terms: 8.8141931 + 0.3 = 9.1141931 x = 9.1141931 Simplifying x = 9.1141931

Subproblem 2

x + -0.3 = -8.8141931 Simplifying x + -0.3 = -8.8141931 Reorder the terms: -0.3 + x = -8.8141931 Solving -0.3 + x = -8.8141931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -8.8141931 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -8.8141931 + 0.3 x = -8.8141931 + 0.3 Combine like terms: -8.8141931 + 0.3 = -8.5141931 x = -8.5141931 Simplifying x = -8.5141931

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.1141931, -8.5141931}

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