8x^2+30x-7=0

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Solution for 8x^2+30x-7=0 equation:


Simplifying
8x2 + 30x + -7 = 0

Reorder the terms:
-7 + 30x + 8x2 = 0

Solving
-7 + 30x + 8x2 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
-0.875 + 3.75x + x2 = 0

Move the constant term to the right:

Add '0.875' to each side of the equation.
-0.875 + 3.75x + 0.875 + x2 = 0 + 0.875

Reorder the terms:
-0.875 + 0.875 + 3.75x + x2 = 0 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + 3.75x + x2 = 0 + 0.875
3.75x + x2 = 0 + 0.875

Combine like terms: 0 + 0.875 = 0.875
3.75x + x2 = 0.875

The x term is 3.75x.  Take half its coefficient (1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
3.75x + 3.515625 + x2 = 0.875 + 3.515625

Reorder the terms:
3.515625 + 3.75x + x2 = 0.875 + 3.515625

Combine like terms: 0.875 + 3.515625 = 4.390625
3.515625 + 3.75x + x2 = 4.390625

Factor a perfect square on the left side:
(x + 1.875)(x + 1.875) = 4.390625

Calculate the square root of the right side: 2.095381827

Break this problem into two subproblems by setting 
(x + 1.875) equal to 2.095381827 and -2.095381827.

Subproblem 1

x + 1.875 = 2.095381827 Simplifying x + 1.875 = 2.095381827 Reorder the terms: 1.875 + x = 2.095381827 Solving 1.875 + x = 2.095381827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = 2.095381827 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 2.095381827 + -1.875 x = 2.095381827 + -1.875 Combine like terms: 2.095381827 + -1.875 = 0.220381827 x = 0.220381827 Simplifying x = 0.220381827

Subproblem 2

x + 1.875 = -2.095381827 Simplifying x + 1.875 = -2.095381827 Reorder the terms: 1.875 + x = -2.095381827 Solving 1.875 + x = -2.095381827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = -2.095381827 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -2.095381827 + -1.875 x = -2.095381827 + -1.875 Combine like terms: -2.095381827 + -1.875 = -3.970381827 x = -3.970381827 Simplifying x = -3.970381827

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.220381827, -3.970381827}

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