=3x^2+7x-16

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Solution for =3x^2+7x-16 equation:


Simplifying
0 = 3x2 + 7x + -16

Reorder the terms:
0 = -16 + 7x + 3x2

Solving
0 = -16 + 7x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + 16 = 16
16 + -7x + -3x2 = -16 + 7x + 3x2 + 16 + -7x + -3x2

Reorder the terms:
16 + -7x + -3x2 = -16 + 16 + 7x + -7x + 3x2 + -3x2

Combine like terms: -16 + 16 = 0
16 + -7x + -3x2 = 0 + 7x + -7x + 3x2 + -3x2
16 + -7x + -3x2 = 7x + -7x + 3x2 + -3x2

Combine like terms: 7x + -7x = 0
16 + -7x + -3x2 = 0 + 3x2 + -3x2
16 + -7x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
16 + -7x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-5.333333333 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '5.333333333' to each side of the equation.
-5.333333333 + 2.333333333x + 5.333333333 + x2 = 0 + 5.333333333

Reorder the terms:
-5.333333333 + 5.333333333 + 2.333333333x + x2 = 0 + 5.333333333

Combine like terms: -5.333333333 + 5.333333333 = 0.000000000
0.000000000 + 2.333333333x + x2 = 0 + 5.333333333
2.333333333x + x2 = 0 + 5.333333333

Combine like terms: 0 + 5.333333333 = 5.333333333
2.333333333x + x2 = 5.333333333

The x term is 2.333333333x.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333x + 1.361111112 + x2 = 5.333333333 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = 5.333333333 + 1.361111112

Combine like terms: 5.333333333 + 1.361111112 = 6.694444445
1.361111112 + 2.333333333x + x2 = 6.694444445

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = 6.694444445

Calculate the square root of the right side: 2.587362449

Break this problem into two subproblems by setting 
(x + 1.166666667) equal to 2.587362449 and -2.587362449.

Subproblem 1

x + 1.166666667 = 2.587362449 Simplifying x + 1.166666667 = 2.587362449 Reorder the terms: 1.166666667 + x = 2.587362449 Solving 1.166666667 + x = 2.587362449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = 2.587362449 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 2.587362449 + -1.166666667 x = 2.587362449 + -1.166666667 Combine like terms: 2.587362449 + -1.166666667 = 1.420695782 x = 1.420695782 Simplifying x = 1.420695782

Subproblem 2

x + 1.166666667 = -2.587362449 Simplifying x + 1.166666667 = -2.587362449 Reorder the terms: 1.166666667 + x = -2.587362449 Solving 1.166666667 + x = -2.587362449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = -2.587362449 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -2.587362449 + -1.166666667 x = -2.587362449 + -1.166666667 Combine like terms: -2.587362449 + -1.166666667 = -3.754029116 x = -3.754029116 Simplifying x = -3.754029116

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.420695782, -3.754029116}

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