10x*10x+x+7=10

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Solution for 10x*10x+x+7=10 equation:


Simplifying
10x * 10x + x + 7 = 10

Reorder the terms for easier multiplication:
10 * 10x * x + x + 7 = 10

Multiply 10 * 10
100x * x + x + 7 = 10

Multiply x * x
100x2 + x + 7 = 10

Reorder the terms:
7 + x + 100x2 = 10

Solving
7 + x + 100x2 = 10

Solving for variable 'x'.

Reorder the terms:
7 + -10 + x + 100x2 = 10 + -10

Combine like terms: 7 + -10 = -3
-3 + x + 100x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-3 + x + 100x2 = 0

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

Divide each side by '100'.
-0.03 + 0.01x + x2 = 0.00

Move the constant term to the right:

Add '0.03' to each side of the equation.
-0.03 + 0.01x + 0.03 + x2 = 0.00 + 0.03

Reorder the terms:
-0.03 + 0.03 + 0.01x + x2 = 0.00 + 0.03

Combine like terms: -0.03 + 0.03 = 0.00
0.00 + 0.01x + x2 = 0.00 + 0.03
0.01x + x2 = 0.00 + 0.03

Combine like terms: 0.00 + 0.03 = 0.03
0.01x + x2 = 0.03

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.01x + 0.25 + x2 = 0.03 + 0.25

Reorder the terms:
0.25 + 0.01x + x2 = 0.03 + 0.25

Combine like terms: 0.03 + 0.25 = 0.28
0.25 + 0.01x + x2 = 0.28

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.28

Calculate the square root of the right side: 0.529150262

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.529150262 and -0.529150262.

Subproblem 1

x + 0.5 = 0.529150262 Simplifying x + 0.5 = 0.529150262 Reorder the terms: 0.5 + x = 0.529150262 Solving 0.5 + x = 0.529150262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.529150262 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.529150262 + -0.5 x = 0.529150262 + -0.5 Combine like terms: 0.529150262 + -0.5 = 0.029150262 x = 0.029150262 Simplifying x = 0.029150262

Subproblem 2

x + 0.5 = -0.529150262 Simplifying x + 0.5 = -0.529150262 Reorder the terms: 0.5 + x = -0.529150262 Solving 0.5 + x = -0.529150262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.529150262 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.529150262 + -0.5 x = -0.529150262 + -0.5 Combine like terms: -0.529150262 + -0.5 = -1.029150262 x = -1.029150262 Simplifying x = -1.029150262

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.029150262, -1.029150262}

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