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Simplifying 14x2 + -46x + -12 = 0 Reorder the terms: -12 + -46x + 14x2 = 0 Solving -12 + -46x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + -23x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -23x + 7x2)' equal to zero and attempt to solve: Simplifying -6 + -23x + 7x2 = 0 Solving -6 + -23x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.8571428571 + -3.285714286x + x2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + -3.285714286x + 0.8571428571 + x2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + -3.285714286x + x2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + -3.285714286x + x2 = 0 + 0.8571428571 -3.285714286x + x2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 -3.285714286x + x2 = 0.8571428571 The x term is -3.285714286x. Take half its coefficient (-1.642857143). Square it (2.698979592) and add it to both sides. Add '2.698979592' to each side of the equation. -3.285714286x + 2.698979592 + x2 = 0.8571428571 + 2.698979592 Reorder the terms: 2.698979592 + -3.285714286x + x2 = 0.8571428571 + 2.698979592 Combine like terms: 0.8571428571 + 2.698979592 = 3.5561224491 2.698979592 + -3.285714286x + x2 = 3.5561224491 Factor a perfect square on the left side: (x + -1.642857143)(x + -1.642857143) = 3.5561224491 Calculate the square root of the right side: 1.885768398 Break this problem into two subproblems by setting (x + -1.642857143) equal to 1.885768398 and -1.885768398.Subproblem 1
x + -1.642857143 = 1.885768398 Simplifying x + -1.642857143 = 1.885768398 Reorder the terms: -1.642857143 + x = 1.885768398 Solving -1.642857143 + x = 1.885768398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.642857143' to each side of the equation. -1.642857143 + 1.642857143 + x = 1.885768398 + 1.642857143 Combine like terms: -1.642857143 + 1.642857143 = 0.000000000 0.000000000 + x = 1.885768398 + 1.642857143 x = 1.885768398 + 1.642857143 Combine like terms: 1.885768398 + 1.642857143 = 3.528625541 x = 3.528625541 Simplifying x = 3.528625541Subproblem 2
x + -1.642857143 = -1.885768398 Simplifying x + -1.642857143 = -1.885768398 Reorder the terms: -1.642857143 + x = -1.885768398 Solving -1.642857143 + x = -1.885768398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.642857143' to each side of the equation. -1.642857143 + 1.642857143 + x = -1.885768398 + 1.642857143 Combine like terms: -1.642857143 + 1.642857143 = 0.000000000 0.000000000 + x = -1.885768398 + 1.642857143 x = -1.885768398 + 1.642857143 Combine like terms: -1.885768398 + 1.642857143 = -0.242911255 x = -0.242911255 Simplifying x = -0.242911255Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.528625541, -0.242911255}Solution
x = {3.528625541, -0.242911255}
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