7x^2-63x=69

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Solution for 7x^2-63x=69 equation:


Simplifying
7x2 + -63x = 69

Reorder the terms:
-63x + 7x2 = 69

Solving
-63x + 7x2 = 69

Solving for variable 'x'.

Reorder the terms:
-69 + -63x + 7x2 = 69 + -69

Combine like terms: 69 + -69 = 0
-69 + -63x + 7x2 = 0

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

Divide each side by '7'.
-9.857142857 + -9x + x2 = 0

Move the constant term to the right:

Add '9.857142857' to each side of the equation.
-9.857142857 + -9x + 9.857142857 + x2 = 0 + 9.857142857

Reorder the terms:
-9.857142857 + 9.857142857 + -9x + x2 = 0 + 9.857142857

Combine like terms: -9.857142857 + 9.857142857 = 0.000000000
0.000000000 + -9x + x2 = 0 + 9.857142857
-9x + x2 = 0 + 9.857142857

Combine like terms: 0 + 9.857142857 = 9.857142857
-9x + x2 = 9.857142857

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = 9.857142857 + 20.25

Reorder the terms:
20.25 + -9x + x2 = 9.857142857 + 20.25

Combine like terms: 9.857142857 + 20.25 = 30.107142857
20.25 + -9x + x2 = 30.107142857

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 30.107142857

Calculate the square root of the right side: 5.486997618

Break this problem into two subproblems by setting 
(x + -4.5) equal to 5.486997618 and -5.486997618.

Subproblem 1

x + -4.5 = 5.486997618 Simplifying x + -4.5 = 5.486997618 Reorder the terms: -4.5 + x = 5.486997618 Solving -4.5 + x = 5.486997618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 5.486997618 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 5.486997618 + 4.5 x = 5.486997618 + 4.5 Combine like terms: 5.486997618 + 4.5 = 9.986997618 x = 9.986997618 Simplifying x = 9.986997618

Subproblem 2

x + -4.5 = -5.486997618 Simplifying x + -4.5 = -5.486997618 Reorder the terms: -4.5 + x = -5.486997618 Solving -4.5 + x = -5.486997618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -5.486997618 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -5.486997618 + 4.5 x = -5.486997618 + 4.5 Combine like terms: -5.486997618 + 4.5 = -0.986997618 x = -0.986997618 Simplifying x = -0.986997618

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.986997618, -0.986997618}

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