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Simplifying 14x2 + 56x + 4 = 0 Reorder the terms: 4 + 56x + 14x2 = 0 Solving 4 + 56x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + 28x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + 28x + 7x2)' equal to zero and attempt to solve: Simplifying 2 + 28x + 7x2 = 0 Solving 2 + 28x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.2857142857 + 4x + x2 = 0 Move the constant term to the right: Add '-0.2857142857' to each side of the equation. 0.2857142857 + 4x + -0.2857142857 + x2 = 0 + -0.2857142857 Reorder the terms: 0.2857142857 + -0.2857142857 + 4x + x2 = 0 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + 4x + x2 = 0 + -0.2857142857 4x + x2 = 0 + -0.2857142857 Combine like terms: 0 + -0.2857142857 = -0.2857142857 4x + x2 = -0.2857142857 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -0.2857142857 + 4 Reorder the terms: 4 + 4x + x2 = -0.2857142857 + 4 Combine like terms: -0.2857142857 + 4 = 3.7142857143 4 + 4x + x2 = 3.7142857143 Factor a perfect square on the left side: (x + 2)(x + 2) = 3.7142857143 Calculate the square root of the right side: 1.927248223 Break this problem into two subproblems by setting (x + 2) equal to 1.927248223 and -1.927248223.Subproblem 1
x + 2 = 1.927248223 Simplifying x + 2 = 1.927248223 Reorder the terms: 2 + x = 1.927248223 Solving 2 + x = 1.927248223 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.927248223 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.927248223 + -2 x = 1.927248223 + -2 Combine like terms: 1.927248223 + -2 = -0.072751777 x = -0.072751777 Simplifying x = -0.072751777Subproblem 2
x + 2 = -1.927248223 Simplifying x + 2 = -1.927248223 Reorder the terms: 2 + x = -1.927248223 Solving 2 + x = -1.927248223 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.927248223 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.927248223 + -2 x = -1.927248223 + -2 Combine like terms: -1.927248223 + -2 = -3.927248223 x = -3.927248223 Simplifying x = -3.927248223Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.072751777, -3.927248223}Solution
x = {-0.072751777, -3.927248223}
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