8x^2-18x+7=02

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Solution for 8x^2-18x+7=02 equation:


Simplifying
8x2 + -18x + 7 = 2

Reorder the terms:
7 + -18x + 8x2 = 2

Solving
7 + -18x + 8x2 = 2

Solving for variable 'x'.

Reorder the terms:
7 + -2 + -18x + 8x2 = 2 + -2

Combine like terms: 7 + -2 = 5
5 + -18x + 8x2 = 2 + -2

Combine like terms: 2 + -2 = 0
5 + -18x + 8x2 = 0

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

Divide each side by '8'.
0.625 + -2.25x + x2 = 0

Move the constant term to the right:

Add '-0.625' to each side of the equation.
0.625 + -2.25x + -0.625 + x2 = 0 + -0.625

Reorder the terms:
0.625 + -0.625 + -2.25x + x2 = 0 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + -2.25x + x2 = 0 + -0.625
-2.25x + x2 = 0 + -0.625

Combine like terms: 0 + -0.625 = -0.625
-2.25x + x2 = -0.625

The x term is -2.25x.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25x + 1.265625 + x2 = -0.625 + 1.265625

Reorder the terms:
1.265625 + -2.25x + x2 = -0.625 + 1.265625

Combine like terms: -0.625 + 1.265625 = 0.640625
1.265625 + -2.25x + x2 = 0.640625

Factor a perfect square on the left side:
(x + -1.125)(x + -1.125) = 0.640625

Calculate the square root of the right side: 0.80039053

Break this problem into two subproblems by setting 
(x + -1.125) equal to 0.80039053 and -0.80039053.

Subproblem 1

x + -1.125 = 0.80039053 Simplifying x + -1.125 = 0.80039053 Reorder the terms: -1.125 + x = 0.80039053 Solving -1.125 + x = 0.80039053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 0.80039053 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 0.80039053 + 1.125 x = 0.80039053 + 1.125 Combine like terms: 0.80039053 + 1.125 = 1.92539053 x = 1.92539053 Simplifying x = 1.92539053

Subproblem 2

x + -1.125 = -0.80039053 Simplifying x + -1.125 = -0.80039053 Reorder the terms: -1.125 + x = -0.80039053 Solving -1.125 + x = -0.80039053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -0.80039053 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -0.80039053 + 1.125 x = -0.80039053 + 1.125 Combine like terms: -0.80039053 + 1.125 = 0.32460947 x = 0.32460947 Simplifying x = 0.32460947

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.92539053, 0.32460947}

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