-7x^2+9x+7=0

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


Simplifying
-7x2 + 9x + 7 = 0

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

Solving
7 + 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'.
-1 + -1.285714286x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -1.285714286x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -1.285714286x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1.285714286x + x2 = 0 + 1
-1.285714286x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1.285714286x + x2 = 1

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 = 1 + 0.4132653063

Reorder the terms:
0.4132653063 + -1.285714286x + x2 = 1 + 0.4132653063

Combine like terms: 1 + 0.4132653063 = 1.4132653063
0.4132653063 + -1.285714286x + x2 = 1.4132653063

Factor a perfect square on the left side:
(x + -0.642857143)(x + -0.642857143) = 1.4132653063

Calculate the square root of the right side: 1.188808356

Break this problem into two subproblems by setting 
(x + -0.642857143) equal to 1.188808356 and -1.188808356.

Subproblem 1

x + -0.642857143 = 1.188808356 Simplifying x + -0.642857143 = 1.188808356 Reorder the terms: -0.642857143 + x = 1.188808356 Solving -0.642857143 + x = 1.188808356 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 = 1.188808356 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + x = 1.188808356 + 0.642857143 x = 1.188808356 + 0.642857143 Combine like terms: 1.188808356 + 0.642857143 = 1.831665499 x = 1.831665499 Simplifying x = 1.831665499

Subproblem 2

x + -0.642857143 = -1.188808356 Simplifying x + -0.642857143 = -1.188808356 Reorder the terms: -0.642857143 + x = -1.188808356 Solving -0.642857143 + x = -1.188808356 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 = -1.188808356 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + x = -1.188808356 + 0.642857143 x = -1.188808356 + 0.642857143 Combine like terms: -1.188808356 + 0.642857143 = -0.545951213 x = -0.545951213 Simplifying x = -0.545951213

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.831665499, -0.545951213}

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