4x^2+28x+22=0

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Solution for 4x^2+28x+22=0 equation:


Simplifying
4x2 + 28x + 22 = 0

Reorder the terms:
22 + 28x + 4x2 = 0

Solving
22 + 28x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(11 + 14x + 2x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(11 + 14x + 2x2)' equal to zero and attempt to solve: Simplifying 11 + 14x + 2x2 = 0 Solving 11 + 14x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5.5 + 7x + x2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + 7x + -5.5 + x2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + 7x + x2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + 7x + x2 = 0 + -5.5 7x + x2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 7x + x2 = -5.5 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -5.5 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -5.5 + 12.25 Combine like terms: -5.5 + 12.25 = 6.75 12.25 + 7x + x2 = 6.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (x + 3.5) equal to 2.598076211 and -2.598076211.

Subproblem 1

x + 3.5 = 2.598076211 Simplifying x + 3.5 = 2.598076211 Reorder the terms: 3.5 + x = 2.598076211 Solving 3.5 + x = 2.598076211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 2.598076211 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 2.598076211 + -3.5 x = 2.598076211 + -3.5 Combine like terms: 2.598076211 + -3.5 = -0.901923789 x = -0.901923789 Simplifying x = -0.901923789

Subproblem 2

x + 3.5 = -2.598076211 Simplifying x + 3.5 = -2.598076211 Reorder the terms: 3.5 + x = -2.598076211 Solving 3.5 + x = -2.598076211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -2.598076211 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -2.598076211 + -3.5 x = -2.598076211 + -3.5 Combine like terms: -2.598076211 + -3.5 = -6.098076211 x = -6.098076211 Simplifying x = -6.098076211

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.901923789, -6.098076211}

Solution

x = {-0.901923789, -6.098076211}

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