8x^2+12x-30=4x+3

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Solution for 8x^2+12x-30=4x+3 equation:


Simplifying
8x2 + 12x + -30 = 4x + 3

Reorder the terms:
-30 + 12x + 8x2 = 4x + 3

Reorder the terms:
-30 + 12x + 8x2 = 3 + 4x

Solving
-30 + 12x + 8x2 = 3 + 4x

Solving for variable 'x'.

Reorder the terms:
-30 + -3 + 12x + -4x + 8x2 = 3 + 4x + -3 + -4x

Combine like terms: -30 + -3 = -33
-33 + 12x + -4x + 8x2 = 3 + 4x + -3 + -4x

Combine like terms: 12x + -4x = 8x
-33 + 8x + 8x2 = 3 + 4x + -3 + -4x

Reorder the terms:
-33 + 8x + 8x2 = 3 + -3 + 4x + -4x

Combine like terms: 3 + -3 = 0
-33 + 8x + 8x2 = 0 + 4x + -4x
-33 + 8x + 8x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-33 + 8x + 8x2 = 0

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

Divide each side by '8'.
-4.125 + x + x2 = 0

Move the constant term to the right:

Add '4.125' to each side of the equation.
-4.125 + x + 4.125 + x2 = 0 + 4.125

Reorder the terms:
-4.125 + 4.125 + x + x2 = 0 + 4.125

Combine like terms: -4.125 + 4.125 = 0.000
0.000 + x + x2 = 0 + 4.125
x + x2 = 0 + 4.125

Combine like terms: 0 + 4.125 = 4.125
x + x2 = 4.125

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 4.125 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 4.125 + 0.25

Combine like terms: 4.125 + 0.25 = 4.375
1.25 + x2 = 4.375

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 4.375

Calculate the square root of the right side: 2.091650066

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.091650066 and -2.091650066.

Subproblem 1

x + 0.5 = 2.091650066 Simplifying x + 0.5 = 2.091650066 Reorder the terms: 0.5 + x = 2.091650066 Solving 0.5 + x = 2.091650066 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.091650066 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.091650066 + -0.5 x = 2.091650066 + -0.5 Combine like terms: 2.091650066 + -0.5 = 1.591650066 x = 1.591650066 Simplifying x = 1.591650066

Subproblem 2

x + 0.5 = -2.091650066 Simplifying x + 0.5 = -2.091650066 Reorder the terms: 0.5 + x = -2.091650066 Solving 0.5 + x = -2.091650066 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.091650066 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.091650066 + -0.5 x = -2.091650066 + -0.5 Combine like terms: -2.091650066 + -0.5 = -2.591650066 x = -2.591650066 Simplifying x = -2.591650066

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.591650066, -2.591650066}

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