8x^2-6x-17=3x^2

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Solution for 8x^2-6x-17=3x^2 equation:


Simplifying
8x2 + -6x + -17 = 3x2

Reorder the terms:
-17 + -6x + 8x2 = 3x2

Solving
-17 + -6x + 8x2 = 3x2

Solving for variable 'x'.

Combine like terms: 8x2 + -3x2 = 5x2
-17 + -6x + 5x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-17 + -6x + 5x2 = 0

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

Divide each side by '5'.
-3.4 + -1.2x + x2 = 0

Move the constant term to the right:

Add '3.4' to each side of the equation.
-3.4 + -1.2x + 3.4 + x2 = 0 + 3.4

Reorder the terms:
-3.4 + 3.4 + -1.2x + x2 = 0 + 3.4

Combine like terms: -3.4 + 3.4 = 0.0
0.0 + -1.2x + x2 = 0 + 3.4
-1.2x + x2 = 0 + 3.4

Combine like terms: 0 + 3.4 = 3.4
-1.2x + x2 = 3.4

The x term is -1.2x.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2x + 0.36 + x2 = 3.4 + 0.36

Reorder the terms:
0.36 + -1.2x + x2 = 3.4 + 0.36

Combine like terms: 3.4 + 0.36 = 3.76
0.36 + -1.2x + x2 = 3.76

Factor a perfect square on the left side:
(x + -0.6)(x + -0.6) = 3.76

Calculate the square root of the right side: 1.939071943

Break this problem into two subproblems by setting 
(x + -0.6) equal to 1.939071943 and -1.939071943.

Subproblem 1

x + -0.6 = 1.939071943 Simplifying x + -0.6 = 1.939071943 Reorder the terms: -0.6 + x = 1.939071943 Solving -0.6 + x = 1.939071943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 1.939071943 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 1.939071943 + 0.6 x = 1.939071943 + 0.6 Combine like terms: 1.939071943 + 0.6 = 2.539071943 x = 2.539071943 Simplifying x = 2.539071943

Subproblem 2

x + -0.6 = -1.939071943 Simplifying x + -0.6 = -1.939071943 Reorder the terms: -0.6 + x = -1.939071943 Solving -0.6 + x = -1.939071943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -1.939071943 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -1.939071943 + 0.6 x = -1.939071943 + 0.6 Combine like terms: -1.939071943 + 0.6 = -1.339071943 x = -1.339071943 Simplifying x = -1.339071943

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.539071943, -1.339071943}

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