4x^2+30x-21=0

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Solution for 4x^2+30x-21=0 equation:


Simplifying
4x2 + 30x + -21 = 0

Reorder the terms:
-21 + 30x + 4x2 = 0

Solving
-21 + 30x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-5.25 + 7.5x + x2 = 0

Move the constant term to the right:

Add '5.25' to each side of the equation.
-5.25 + 7.5x + 5.25 + x2 = 0 + 5.25

Reorder the terms:
-5.25 + 5.25 + 7.5x + x2 = 0 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + 7.5x + x2 = 0 + 5.25
7.5x + x2 = 0 + 5.25

Combine like terms: 0 + 5.25 = 5.25
7.5x + x2 = 5.25

The x term is 7.5x.  Take half its coefficient (3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
7.5x + 14.0625 + x2 = 5.25 + 14.0625

Reorder the terms:
14.0625 + 7.5x + x2 = 5.25 + 14.0625

Combine like terms: 5.25 + 14.0625 = 19.3125
14.0625 + 7.5x + x2 = 19.3125

Factor a perfect square on the left side:
(x + 3.75)(x + 3.75) = 19.3125

Calculate the square root of the right side: 4.394598958

Break this problem into two subproblems by setting 
(x + 3.75) equal to 4.394598958 and -4.394598958.

Subproblem 1

x + 3.75 = 4.394598958 Simplifying x + 3.75 = 4.394598958 Reorder the terms: 3.75 + x = 4.394598958 Solving 3.75 + x = 4.394598958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 4.394598958 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 4.394598958 + -3.75 x = 4.394598958 + -3.75 Combine like terms: 4.394598958 + -3.75 = 0.644598958 x = 0.644598958 Simplifying x = 0.644598958

Subproblem 2

x + 3.75 = -4.394598958 Simplifying x + 3.75 = -4.394598958 Reorder the terms: 3.75 + x = -4.394598958 Solving 3.75 + x = -4.394598958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -4.394598958 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -4.394598958 + -3.75 x = -4.394598958 + -3.75 Combine like terms: -4.394598958 + -3.75 = -8.144598958 x = -8.144598958 Simplifying x = -8.144598958

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.644598958, -8.144598958}

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