7x^2-9x-120=0

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Solution for 7x^2-9x-120=0 equation:


Simplifying
7x2 + -9x + -120 = 0

Reorder the terms:
-120 + -9x + 7x2 = 0

Solving
-120 + -9x + 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'.
-17.14285714 + -1.285714286x + x2 = 0

Move the constant term to the right:

Add '17.14285714' to each side of the equation.
-17.14285714 + -1.285714286x + 17.14285714 + x2 = 0 + 17.14285714

Reorder the terms:
-17.14285714 + 17.14285714 + -1.285714286x + x2 = 0 + 17.14285714

Combine like terms: -17.14285714 + 17.14285714 = 0.00000000
0.00000000 + -1.285714286x + x2 = 0 + 17.14285714
-1.285714286x + x2 = 0 + 17.14285714

Combine like terms: 0 + 17.14285714 = 17.14285714
-1.285714286x + x2 = 17.14285714

The x term is -1.285714286x.  Take half its coefficient (-0.642857143).
Square it (0.4132653063) and add it to both sides.

Add '0.4132653063' to each side of the equation.
-1.285714286x + 0.4132653063 + x2 = 17.14285714 + 0.4132653063

Reorder the terms:
0.4132653063 + -1.285714286x + x2 = 17.14285714 + 0.4132653063

Combine like terms: 17.14285714 + 0.4132653063 = 17.5561224463
0.4132653063 + -1.285714286x + x2 = 17.5561224463

Factor a perfect square on the left side:
(x + -0.642857143)(x + -0.642857143) = 17.5561224463

Calculate the square root of the right side: 4.190002679

Break this problem into two subproblems by setting 
(x + -0.642857143) equal to 4.190002679 and -4.190002679.

Subproblem 1

x + -0.642857143 = 4.190002679 Simplifying x + -0.642857143 = 4.190002679 Reorder the terms: -0.642857143 + x = 4.190002679 Solving -0.642857143 + x = 4.190002679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + x = 4.190002679 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + x = 4.190002679 + 0.642857143 x = 4.190002679 + 0.642857143 Combine like terms: 4.190002679 + 0.642857143 = 4.832859822 x = 4.832859822 Simplifying x = 4.832859822

Subproblem 2

x + -0.642857143 = -4.190002679 Simplifying x + -0.642857143 = -4.190002679 Reorder the terms: -0.642857143 + x = -4.190002679 Solving -0.642857143 + x = -4.190002679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + x = -4.190002679 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + x = -4.190002679 + 0.642857143 x = -4.190002679 + 0.642857143 Combine like terms: -4.190002679 + 0.642857143 = -3.547145536 x = -3.547145536 Simplifying x = -3.547145536

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.832859822, -3.547145536}

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