7x^2-14x-78=-9

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Solution for 7x^2-14x-78=-9 equation:


Simplifying
7x2 + -14x + -78 = -9

Reorder the terms:
-78 + -14x + 7x2 = -9

Solving
-78 + -14x + 7x2 = -9

Solving for variable 'x'.

Reorder the terms:
-78 + 9 + -14x + 7x2 = -9 + 9

Combine like terms: -78 + 9 = -69
-69 + -14x + 7x2 = -9 + 9

Combine like terms: -9 + 9 = 0
-69 + -14x + 7x2 = 0

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

Divide each side by '7'.
-9.857142857 + -2x + x2 = 0

Move the constant term to the right:

Add '9.857142857' to each side of the equation.
-9.857142857 + -2x + 9.857142857 + x2 = 0 + 9.857142857

Reorder the terms:
-9.857142857 + 9.857142857 + -2x + x2 = 0 + 9.857142857

Combine like terms: -9.857142857 + 9.857142857 = 0.000000000
0.000000000 + -2x + x2 = 0 + 9.857142857
-2x + x2 = 0 + 9.857142857

Combine like terms: 0 + 9.857142857 = 9.857142857
-2x + x2 = 9.857142857

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 9.857142857 + 1

Reorder the terms:
1 + -2x + x2 = 9.857142857 + 1

Combine like terms: 9.857142857 + 1 = 10.857142857
1 + -2x + x2 = 10.857142857

Factor a perfect square on the left side:
(x + -1)(x + -1) = 10.857142857

Calculate the square root of the right side: 3.295017884

Break this problem into two subproblems by setting 
(x + -1) equal to 3.295017884 and -3.295017884.

Subproblem 1

x + -1 = 3.295017884 Simplifying x + -1 = 3.295017884 Reorder the terms: -1 + x = 3.295017884 Solving -1 + x = 3.295017884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 3.295017884 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.295017884 + 1 x = 3.295017884 + 1 Combine like terms: 3.295017884 + 1 = 4.295017884 x = 4.295017884 Simplifying x = 4.295017884

Subproblem 2

x + -1 = -3.295017884 Simplifying x + -1 = -3.295017884 Reorder the terms: -1 + x = -3.295017884 Solving -1 + x = -3.295017884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -3.295017884 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.295017884 + 1 x = -3.295017884 + 1 Combine like terms: -3.295017884 + 1 = -2.295017884 x = -2.295017884 Simplifying x = -2.295017884

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.295017884, -2.295017884}

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