5x^2+8x-30=

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Solution for 5x^2+8x-30= equation:


Simplifying
5x2 + 8x + -30 = 0

Reorder the terms:
-30 + 8x + 5x2 = 0

Solving
-30 + 8x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-6 + 1.6x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 1.6x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 1.6x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 1.6x + x2 = 0 + 6
1.6x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
1.6x + x2 = 6

The x term is 1.6x.  Take half its coefficient (0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
1.6x + 0.64 + x2 = 6 + 0.64

Reorder the terms:
0.64 + 1.6x + x2 = 6 + 0.64

Combine like terms: 6 + 0.64 = 6.64
0.64 + 1.6x + x2 = 6.64

Factor a perfect square on the left side:
(x + 0.8)(x + 0.8) = 6.64

Calculate the square root of the right side: 2.576819745

Break this problem into two subproblems by setting 
(x + 0.8) equal to 2.576819745 and -2.576819745.

Subproblem 1

x + 0.8 = 2.576819745 Simplifying x + 0.8 = 2.576819745 Reorder the terms: 0.8 + x = 2.576819745 Solving 0.8 + x = 2.576819745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 2.576819745 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 2.576819745 + -0.8 x = 2.576819745 + -0.8 Combine like terms: 2.576819745 + -0.8 = 1.776819745 x = 1.776819745 Simplifying x = 1.776819745

Subproblem 2

x + 0.8 = -2.576819745 Simplifying x + 0.8 = -2.576819745 Reorder the terms: 0.8 + x = -2.576819745 Solving 0.8 + x = -2.576819745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -2.576819745 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -2.576819745 + -0.8 x = -2.576819745 + -0.8 Combine like terms: -2.576819745 + -0.8 = -3.376819745 x = -3.376819745 Simplifying x = -3.376819745

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.776819745, -3.376819745}

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