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Simplifying 28x2 + 36x + 6 = 0 Reorder the terms: 6 + 36x + 28x2 = 0 Solving 6 + 36x + 28x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 18x + 14x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 18x + 14x2)' equal to zero and attempt to solve: Simplifying 3 + 18x + 14x2 = 0 Solving 3 + 18x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 0.2142857143 + 1.285714286x + x2 = 0 Move the constant term to the right: Add '-0.2142857143' to each side of the equation. 0.2142857143 + 1.285714286x + -0.2142857143 + x2 = 0 + -0.2142857143 Reorder the terms: 0.2142857143 + -0.2142857143 + 1.285714286x + x2 = 0 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + 1.285714286x + x2 = 0 + -0.2142857143 1.285714286x + x2 = 0 + -0.2142857143 Combine like terms: 0 + -0.2142857143 = -0.2142857143 1.285714286x + x2 = -0.2142857143 The x term is 1.285714286x. Take half its coefficient (0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. 1.285714286x + 0.4132653063 + x2 = -0.2142857143 + 0.4132653063 Reorder the terms: 0.4132653063 + 1.285714286x + x2 = -0.2142857143 + 0.4132653063 Combine like terms: -0.2142857143 + 0.4132653063 = 0.198979592 0.4132653063 + 1.285714286x + x2 = 0.198979592 Factor a perfect square on the left side: (x + 0.642857143)(x + 0.642857143) = 0.198979592 Calculate the square root of the right side: 0.446071286 Break this problem into two subproblems by setting (x + 0.642857143) equal to 0.446071286 and -0.446071286.Subproblem 1
x + 0.642857143 = 0.446071286 Simplifying x + 0.642857143 = 0.446071286 Reorder the terms: 0.642857143 + x = 0.446071286 Solving 0.642857143 + x = 0.446071286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.642857143' to each side of the equation. 0.642857143 + -0.642857143 + x = 0.446071286 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + x = 0.446071286 + -0.642857143 x = 0.446071286 + -0.642857143 Combine like terms: 0.446071286 + -0.642857143 = -0.196785857 x = -0.196785857 Simplifying x = -0.196785857Subproblem 2
x + 0.642857143 = -0.446071286 Simplifying x + 0.642857143 = -0.446071286 Reorder the terms: 0.642857143 + x = -0.446071286 Solving 0.642857143 + x = -0.446071286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.642857143' to each side of the equation. 0.642857143 + -0.642857143 + x = -0.446071286 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + x = -0.446071286 + -0.642857143 x = -0.446071286 + -0.642857143 Combine like terms: -0.446071286 + -0.642857143 = -1.088928429 x = -1.088928429 Simplifying x = -1.088928429Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.196785857, -1.088928429}Solution
x = {-0.196785857, -1.088928429}
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