(x-10)-9+7x(x-10)=

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Solution for (x-10)-9+7x(x-10)= equation:


Simplifying
(x + -10) + -9 + 7x(x + -10) = 0

Reorder the terms:
(-10 + x) + -9 + 7x(x + -10) = 0

Remove parenthesis around (-10 + x)
-10 + x + -9 + 7x(x + -10) = 0

Reorder the terms:
-10 + x + -9 + 7x(-10 + x) = 0
-10 + x + -9 + (-10 * 7x + x * 7x) = 0
-10 + x + -9 + (-70x + 7x2) = 0

Reorder the terms:
-10 + -9 + x + -70x + 7x2 = 0

Combine like terms: -10 + -9 = -19
-19 + x + -70x + 7x2 = 0

Combine like terms: x + -70x = -69x
-19 + -69x + 7x2 = 0

Solving
-19 + -69x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-2.714285714 + -9.857142857x + x2 = 0

Move the constant term to the right:

Add '2.714285714' to each side of the equation.
-2.714285714 + -9.857142857x + 2.714285714 + x2 = 0 + 2.714285714

Reorder the terms:
-2.714285714 + 2.714285714 + -9.857142857x + x2 = 0 + 2.714285714

Combine like terms: -2.714285714 + 2.714285714 = 0.000000000
0.000000000 + -9.857142857x + x2 = 0 + 2.714285714
-9.857142857x + x2 = 0 + 2.714285714

Combine like terms: 0 + 2.714285714 = 2.714285714
-9.857142857x + x2 = 2.714285714

The x term is -9.857142857x.  Take half its coefficient (-4.928571429).
Square it (24.29081633) and add it to both sides.

Add '24.29081633' to each side of the equation.
-9.857142857x + 24.29081633 + x2 = 2.714285714 + 24.29081633

Reorder the terms:
24.29081633 + -9.857142857x + x2 = 2.714285714 + 24.29081633

Combine like terms: 2.714285714 + 24.29081633 = 27.005102044
24.29081633 + -9.857142857x + x2 = 27.005102044

Factor a perfect square on the left side:
(x + -4.928571429)(x + -4.928571429) = 27.005102044

Calculate the square root of the right side: 5.196643344

Break this problem into two subproblems by setting 
(x + -4.928571429) equal to 5.196643344 and -5.196643344.

Subproblem 1

x + -4.928571429 = 5.196643344 Simplifying x + -4.928571429 = 5.196643344 Reorder the terms: -4.928571429 + x = 5.196643344 Solving -4.928571429 + x = 5.196643344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.928571429' to each side of the equation. -4.928571429 + 4.928571429 + x = 5.196643344 + 4.928571429 Combine like terms: -4.928571429 + 4.928571429 = 0.000000000 0.000000000 + x = 5.196643344 + 4.928571429 x = 5.196643344 + 4.928571429 Combine like terms: 5.196643344 + 4.928571429 = 10.125214773 x = 10.125214773 Simplifying x = 10.125214773

Subproblem 2

x + -4.928571429 = -5.196643344 Simplifying x + -4.928571429 = -5.196643344 Reorder the terms: -4.928571429 + x = -5.196643344 Solving -4.928571429 + x = -5.196643344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.928571429' to each side of the equation. -4.928571429 + 4.928571429 + x = -5.196643344 + 4.928571429 Combine like terms: -4.928571429 + 4.928571429 = 0.000000000 0.000000000 + x = -5.196643344 + 4.928571429 x = -5.196643344 + 4.928571429 Combine like terms: -5.196643344 + 4.928571429 = -0.268071915 x = -0.268071915 Simplifying x = -0.268071915

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.125214773, -0.268071915}

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