-7x^2-4x+8=0

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Solution for -7x^2-4x+8=0 equation:


Simplifying
-7x2 + -4x + 8 = 0

Reorder the terms:
8 + -4x + -7x2 = 0

Solving
8 + -4x + -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'.
-1.142857143 + 0.5714285714x + x2 = 0

Move the constant term to the right:

Add '1.142857143' to each side of the equation.
-1.142857143 + 0.5714285714x + 1.142857143 + x2 = 0 + 1.142857143

Reorder the terms:
-1.142857143 + 1.142857143 + 0.5714285714x + x2 = 0 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + 0.5714285714x + x2 = 0 + 1.142857143
0.5714285714x + x2 = 0 + 1.142857143

Combine like terms: 0 + 1.142857143 = 1.142857143
0.5714285714x + x2 = 1.142857143

The x term is 0.5714285714x.  Take half its coefficient (0.2857142857).
Square it (0.08163265305) and add it to both sides.

Add '0.08163265305' to each side of the equation.
0.5714285714x + 0.08163265305 + x2 = 1.142857143 + 0.08163265305

Reorder the terms:
0.08163265305 + 0.5714285714x + x2 = 1.142857143 + 0.08163265305

Combine like terms: 1.142857143 + 0.08163265305 = 1.22448979605
0.08163265305 + 0.5714285714x + x2 = 1.22448979605

Factor a perfect square on the left side:
(x + 0.2857142857)(x + 0.2857142857) = 1.22448979605

Calculate the square root of the right side: 1.10656667

Break this problem into two subproblems by setting 
(x + 0.2857142857) equal to 1.10656667 and -1.10656667.

Subproblem 1

x + 0.2857142857 = 1.10656667 Simplifying x + 0.2857142857 = 1.10656667 Reorder the terms: 0.2857142857 + x = 1.10656667 Solving 0.2857142857 + x = 1.10656667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = 1.10656667 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = 1.10656667 + -0.2857142857 x = 1.10656667 + -0.2857142857 Combine like terms: 1.10656667 + -0.2857142857 = 0.8208523843 x = 0.8208523843 Simplifying x = 0.8208523843

Subproblem 2

x + 0.2857142857 = -1.10656667 Simplifying x + 0.2857142857 = -1.10656667 Reorder the terms: 0.2857142857 + x = -1.10656667 Solving 0.2857142857 + x = -1.10656667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = -1.10656667 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = -1.10656667 + -0.2857142857 x = -1.10656667 + -0.2857142857 Combine like terms: -1.10656667 + -0.2857142857 = -1.3922809557 x = -1.3922809557 Simplifying x = -1.3922809557

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.8208523843, -1.3922809557}

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