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Simplifying 14x2 + -74x + 12 = 0 Reorder the terms: 12 + -74x + 14x2 = 0 Solving 12 + -74x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -37x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + -37x + 7x2)' equal to zero and attempt to solve: Simplifying 6 + -37x + 7x2 = 0 Solving 6 + -37x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.8571428571 + -5.285714286x + x2 = 0 Move the constant term to the right: Add '-0.8571428571' to each side of the equation. 0.8571428571 + -5.285714286x + -0.8571428571 + x2 = 0 + -0.8571428571 Reorder the terms: 0.8571428571 + -0.8571428571 + -5.285714286x + x2 = 0 + -0.8571428571 Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000 0.0000000000 + -5.285714286x + x2 = 0 + -0.8571428571 -5.285714286x + x2 = 0 + -0.8571428571 Combine like terms: 0 + -0.8571428571 = -0.8571428571 -5.285714286x + x2 = -0.8571428571 The x term is -5.285714286x. Take half its coefficient (-2.642857143). Square it (6.984693878) and add it to both sides. Add '6.984693878' to each side of the equation. -5.285714286x + 6.984693878 + x2 = -0.8571428571 + 6.984693878 Reorder the terms: 6.984693878 + -5.285714286x + x2 = -0.8571428571 + 6.984693878 Combine like terms: -0.8571428571 + 6.984693878 = 6.1275510209 6.984693878 + -5.285714286x + x2 = 6.1275510209 Factor a perfect square on the left side: (x + -2.642857143)(x + -2.642857143) = 6.1275510209 Calculate the square root of the right side: 2.475389065 Break this problem into two subproblems by setting (x + -2.642857143) equal to 2.475389065 and -2.475389065.Subproblem 1
x + -2.642857143 = 2.475389065 Simplifying x + -2.642857143 = 2.475389065 Reorder the terms: -2.642857143 + x = 2.475389065 Solving -2.642857143 + x = 2.475389065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.642857143' to each side of the equation. -2.642857143 + 2.642857143 + x = 2.475389065 + 2.642857143 Combine like terms: -2.642857143 + 2.642857143 = 0.000000000 0.000000000 + x = 2.475389065 + 2.642857143 x = 2.475389065 + 2.642857143 Combine like terms: 2.475389065 + 2.642857143 = 5.118246208 x = 5.118246208 Simplifying x = 5.118246208Subproblem 2
x + -2.642857143 = -2.475389065 Simplifying x + -2.642857143 = -2.475389065 Reorder the terms: -2.642857143 + x = -2.475389065 Solving -2.642857143 + x = -2.475389065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.642857143' to each side of the equation. -2.642857143 + 2.642857143 + x = -2.475389065 + 2.642857143 Combine like terms: -2.642857143 + 2.642857143 = 0.000000000 0.000000000 + x = -2.475389065 + 2.642857143 x = -2.475389065 + 2.642857143 Combine like terms: -2.475389065 + 2.642857143 = 0.167468078 x = 0.167468078 Simplifying x = 0.167468078Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.118246208, 0.167468078}Solution
x = {5.118246208, 0.167468078}
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