4x^2+3x=400

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Solution for 4x^2+3x=400 equation:


Simplifying
4x2 + 3x = 400

Reorder the terms:
3x + 4x2 = 400

Solving
3x + 4x2 = 400

Solving for variable 'x'.

Reorder the terms:
-400 + 3x + 4x2 = 400 + -400

Combine like terms: 400 + -400 = 0
-400 + 3x + 4x2 = 0

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

Divide each side by '4'.
-100 + 0.75x + x2 = 0

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 0.75x + 100 + x2 = 0 + 100

Reorder the terms:
-100 + 100 + 0.75x + x2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 0.75x + x2 = 0 + 100
0.75x + x2 = 0 + 100

Combine like terms: 0 + 100 = 100
0.75x + x2 = 100

The x term is 0.75x.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x + 0.140625 + x2 = 100 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = 100 + 0.140625

Combine like terms: 100 + 0.140625 = 100.140625
0.140625 + 0.75x + x2 = 100.140625

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = 100.140625

Calculate the square root of the right side: 10.00702878

Break this problem into two subproblems by setting 
(x + 0.375) equal to 10.00702878 and -10.00702878.

Subproblem 1

x + 0.375 = 10.00702878 Simplifying x + 0.375 = 10.00702878 Reorder the terms: 0.375 + x = 10.00702878 Solving 0.375 + x = 10.00702878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 10.00702878 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 10.00702878 + -0.375 x = 10.00702878 + -0.375 Combine like terms: 10.00702878 + -0.375 = 9.63202878 x = 9.63202878 Simplifying x = 9.63202878

Subproblem 2

x + 0.375 = -10.00702878 Simplifying x + 0.375 = -10.00702878 Reorder the terms: 0.375 + x = -10.00702878 Solving 0.375 + x = -10.00702878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -10.00702878 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -10.00702878 + -0.375 x = -10.00702878 + -0.375 Combine like terms: -10.00702878 + -0.375 = -10.38202878 x = -10.38202878 Simplifying x = -10.38202878

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.63202878, -10.38202878}

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