8x+10x^2-6=17x

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Solution for 8x+10x^2-6=17x equation:


Simplifying
8x + 10x2 + -6 = 17x

Reorder the terms:
-6 + 8x + 10x2 = 17x

Solving
-6 + 8x + 10x2 = 17x

Solving for variable 'x'.

Reorder the terms:
-6 + 8x + -17x + 10x2 = 17x + -17x

Combine like terms: 8x + -17x = -9x
-6 + -9x + 10x2 = 17x + -17x

Combine like terms: 17x + -17x = 0
-6 + -9x + 10x2 = 0

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

Divide each side by '10'.
-0.6 + -0.9x + x2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -0.9x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -0.9x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -0.9x + x2 = 0 + 0.6
-0.9x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-0.9x + x2 = 0.6

The x term is -0.9x.  Take half its coefficient (-0.45).
Square it (0.2025) and add it to both sides.

Add '0.2025' to each side of the equation.
-0.9x + 0.2025 + x2 = 0.6 + 0.2025

Reorder the terms:
0.2025 + -0.9x + x2 = 0.6 + 0.2025

Combine like terms: 0.6 + 0.2025 = 0.8025
0.2025 + -0.9x + x2 = 0.8025

Factor a perfect square on the left side:
(x + -0.45)(x + -0.45) = 0.8025

Calculate the square root of the right side: 0.895823643

Break this problem into two subproblems by setting 
(x + -0.45) equal to 0.895823643 and -0.895823643.

Subproblem 1

x + -0.45 = 0.895823643 Simplifying x + -0.45 = 0.895823643 Reorder the terms: -0.45 + x = 0.895823643 Solving -0.45 + x = 0.895823643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + x = 0.895823643 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x = 0.895823643 + 0.45 x = 0.895823643 + 0.45 Combine like terms: 0.895823643 + 0.45 = 1.345823643 x = 1.345823643 Simplifying x = 1.345823643

Subproblem 2

x + -0.45 = -0.895823643 Simplifying x + -0.45 = -0.895823643 Reorder the terms: -0.45 + x = -0.895823643 Solving -0.45 + x = -0.895823643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + x = -0.895823643 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x = -0.895823643 + 0.45 x = -0.895823643 + 0.45 Combine like terms: -0.895823643 + 0.45 = -0.445823643 x = -0.445823643 Simplifying x = -0.445823643

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.345823643, -0.445823643}

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