10x^2-24x-876=9.2

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Solution for 10x^2-24x-876=9.2 equation:


Simplifying
10x2 + -24x + -876 = 9.2

Reorder the terms:
-876 + -24x + 10x2 = 9.2

Solving
-876 + -24x + 10x2 = 9.2

Solving for variable 'x'.

Reorder the terms:
-876 + -9.2 + -24x + 10x2 = 9.2 + -9.2

Combine like terms: -876 + -9.2 = -885.2
-885.2 + -24x + 10x2 = 9.2 + -9.2

Combine like terms: 9.2 + -9.2 = 0.0
-885.2 + -24x + 10x2 = 0.0

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

Divide each side by '10'.
-88.52 + -2.4x + x2 = 0.0

Move the constant term to the right:

Add '88.52' to each side of the equation.
-88.52 + -2.4x + 88.52 + x2 = 0.0 + 88.52

Reorder the terms:
-88.52 + 88.52 + -2.4x + x2 = 0.0 + 88.52

Combine like terms: -88.52 + 88.52 = 0.00
0.00 + -2.4x + x2 = 0.0 + 88.52
-2.4x + x2 = 0.0 + 88.52

Combine like terms: 0.0 + 88.52 = 88.52
-2.4x + x2 = 88.52

The x term is -2.4x.  Take half its coefficient (-1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
-2.4x + 1.44 + x2 = 88.52 + 1.44

Reorder the terms:
1.44 + -2.4x + x2 = 88.52 + 1.44

Combine like terms: 88.52 + 1.44 = 89.96
1.44 + -2.4x + x2 = 89.96

Factor a perfect square on the left side:
(x + -1.2)(x + -1.2) = 89.96

Calculate the square root of the right side: 9.484724561

Break this problem into two subproblems by setting 
(x + -1.2) equal to 9.484724561 and -9.484724561.

Subproblem 1

x + -1.2 = 9.484724561 Simplifying x + -1.2 = 9.484724561 Reorder the terms: -1.2 + x = 9.484724561 Solving -1.2 + x = 9.484724561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 9.484724561 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 9.484724561 + 1.2 x = 9.484724561 + 1.2 Combine like terms: 9.484724561 + 1.2 = 10.684724561 x = 10.684724561 Simplifying x = 10.684724561

Subproblem 2

x + -1.2 = -9.484724561 Simplifying x + -1.2 = -9.484724561 Reorder the terms: -1.2 + x = -9.484724561 Solving -1.2 + x = -9.484724561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -9.484724561 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -9.484724561 + 1.2 x = -9.484724561 + 1.2 Combine like terms: -9.484724561 + 1.2 = -8.284724561 x = -8.284724561 Simplifying x = -8.284724561

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.684724561, -8.284724561}

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