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Simplifying 7X2 + -23X = 6 Reorder the terms: -23X + 7X2 = 6 Solving -23X + 7X2 = 6 Solving for variable 'X'. Reorder the terms: -6 + -23X + 7X2 = 6 + -6 Combine like terms: 6 + -6 = 0 -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}
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