x^2-0.7x+0.1=1

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Solution for x^2-0.7x+0.1=1 equation:


Simplifying
x2 + -0.7x + 0.1 = 1

Reorder the terms:
0.1 + -0.7x + x2 = 1

Solving
0.1 + -0.7x + x2 = 1

Solving for variable 'x'.

Reorder the terms:
0.1 + -1 + -0.7x + x2 = 1 + -1

Combine like terms: 0.1 + -1 = -0.9
-0.9 + -0.7x + x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-0.9 + -0.7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '0.9' to each side of the equation.
-0.9 + -0.7x + 0.9 + x2 = 0 + 0.9

Reorder the terms:
-0.9 + 0.9 + -0.7x + x2 = 0 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + -0.7x + x2 = 0 + 0.9
-0.7x + x2 = 0 + 0.9

Combine like terms: 0 + 0.9 = 0.9
-0.7x + x2 = 0.9

The x term is -0.7x.  Take half its coefficient (-0.35).
Square it (0.1225) and add it to both sides.

Add '0.1225' to each side of the equation.
-0.7x + 0.1225 + x2 = 0.9 + 0.1225

Reorder the terms:
0.1225 + -0.7x + x2 = 0.9 + 0.1225

Combine like terms: 0.9 + 0.1225 = 1.0225
0.1225 + -0.7x + x2 = 1.0225

Factor a perfect square on the left side:
(x + -0.35)(x + -0.35) = 1.0225

Calculate the square root of the right side: 1.011187421

Break this problem into two subproblems by setting 
(x + -0.35) equal to 1.011187421 and -1.011187421.

Subproblem 1

x + -0.35 = 1.011187421 Simplifying x + -0.35 = 1.011187421 Reorder the terms: -0.35 + x = 1.011187421 Solving -0.35 + x = 1.011187421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + x = 1.011187421 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = 1.011187421 + 0.35 x = 1.011187421 + 0.35 Combine like terms: 1.011187421 + 0.35 = 1.361187421 x = 1.361187421 Simplifying x = 1.361187421

Subproblem 2

x + -0.35 = -1.011187421 Simplifying x + -0.35 = -1.011187421 Reorder the terms: -0.35 + x = -1.011187421 Solving -0.35 + x = -1.011187421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + x = -1.011187421 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = -1.011187421 + 0.35 x = -1.011187421 + 0.35 Combine like terms: -1.011187421 + 0.35 = -0.661187421 x = -0.661187421 Simplifying x = -0.661187421

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.361187421, -0.661187421}

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