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Simplifying 7x2 + -23x + -38 = 0 Reorder the terms: -38 + -23x + 7x2 = 0 Solving -38 + -23x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -5.428571429 + -3.285714286x + x2 = 0 Move the constant term to the right: Add '5.428571429' to each side of the equation. -5.428571429 + -3.285714286x + 5.428571429 + x2 = 0 + 5.428571429 Reorder the terms: -5.428571429 + 5.428571429 + -3.285714286x + x2 = 0 + 5.428571429 Combine like terms: -5.428571429 + 5.428571429 = 0.000000000 0.000000000 + -3.285714286x + x2 = 0 + 5.428571429 -3.285714286x + x2 = 0 + 5.428571429 Combine like terms: 0 + 5.428571429 = 5.428571429 -3.285714286x + x2 = 5.428571429 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 = 5.428571429 + 2.698979592 Reorder the terms: 2.698979592 + -3.285714286x + x2 = 5.428571429 + 2.698979592 Combine like terms: 5.428571429 + 2.698979592 = 8.127551021 2.698979592 + -3.285714286x + x2 = 8.127551021 Factor a perfect square on the left side: (x + -1.642857143)(x + -1.642857143) = 8.127551021 Calculate the square root of the right side: 2.850886006 Break this problem into two subproblems by setting (x + -1.642857143) equal to 2.850886006 and -2.850886006.Subproblem 1
x + -1.642857143 = 2.850886006 Simplifying x + -1.642857143 = 2.850886006 Reorder the terms: -1.642857143 + x = 2.850886006 Solving -1.642857143 + x = 2.850886006 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 = 2.850886006 + 1.642857143 Combine like terms: -1.642857143 + 1.642857143 = 0.000000000 0.000000000 + x = 2.850886006 + 1.642857143 x = 2.850886006 + 1.642857143 Combine like terms: 2.850886006 + 1.642857143 = 4.493743149 x = 4.493743149 Simplifying x = 4.493743149Subproblem 2
x + -1.642857143 = -2.850886006 Simplifying x + -1.642857143 = -2.850886006 Reorder the terms: -1.642857143 + x = -2.850886006 Solving -1.642857143 + x = -2.850886006 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 = -2.850886006 + 1.642857143 Combine like terms: -1.642857143 + 1.642857143 = 0.000000000 0.000000000 + x = -2.850886006 + 1.642857143 x = -2.850886006 + 1.642857143 Combine like terms: -2.850886006 + 1.642857143 = -1.208028863 x = -1.208028863 Simplifying x = -1.208028863Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.493743149, -1.208028863}
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