3x^2+5x-400=0

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Solution for 3x^2+5x-400=0 equation:


Simplifying
3x2 + 5x + -400 = 0

Reorder the terms:
-400 + 5x + 3x2 = 0

Solving
-400 + 5x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-133.3333333 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '133.3333333' to each side of the equation.
-133.3333333 + 1.666666667x + 133.3333333 + x2 = 0 + 133.3333333

Reorder the terms:
-133.3333333 + 133.3333333 + 1.666666667x + x2 = 0 + 133.3333333

Combine like terms: -133.3333333 + 133.3333333 = 0.0000000
0.0000000 + 1.666666667x + x2 = 0 + 133.3333333
1.666666667x + x2 = 0 + 133.3333333

Combine like terms: 0 + 133.3333333 = 133.3333333
1.666666667x + x2 = 133.3333333

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 133.3333333 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 133.3333333 + 0.6944444447

Combine like terms: 133.3333333 + 0.6944444447 = 134.0277777447
0.6944444447 + 1.666666667x + x2 = 134.0277777447

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 134.0277777447

Calculate the square root of the right side: 11.577036656

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 11.577036656 and -11.577036656.

Subproblem 1

x + 0.8333333335 = 11.577036656 Simplifying x + 0.8333333335 = 11.577036656 Reorder the terms: 0.8333333335 + x = 11.577036656 Solving 0.8333333335 + x = 11.577036656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 11.577036656 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 11.577036656 + -0.8333333335 x = 11.577036656 + -0.8333333335 Combine like terms: 11.577036656 + -0.8333333335 = 10.7437033225 x = 10.7437033225 Simplifying x = 10.7437033225

Subproblem 2

x + 0.8333333335 = -11.577036656 Simplifying x + 0.8333333335 = -11.577036656 Reorder the terms: 0.8333333335 + x = -11.577036656 Solving 0.8333333335 + x = -11.577036656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -11.577036656 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -11.577036656 + -0.8333333335 x = -11.577036656 + -0.8333333335 Combine like terms: -11.577036656 + -0.8333333335 = -12.4103699895 x = -12.4103699895 Simplifying x = -12.4103699895

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.7437033225, -12.4103699895}

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