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Simplifying x2 + -23x + -47 = 0 Reorder the terms: -47 + -23x + x2 = 0 Solving -47 + -23x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + -23x + 47 + x2 = 0 + 47 Reorder the terms: -47 + 47 + -23x + x2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + -23x + x2 = 0 + 47 -23x + x2 = 0 + 47 Combine like terms: 0 + 47 = 47 -23x + x2 = 47 The x term is -23x. Take half its coefficient (-11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. -23x + 132.25 + x2 = 47 + 132.25 Reorder the terms: 132.25 + -23x + x2 = 47 + 132.25 Combine like terms: 47 + 132.25 = 179.25 132.25 + -23x + x2 = 179.25 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 179.25 Calculate the square root of the right side: 13.388427839 Break this problem into two subproblems by setting (x + -11.5) equal to 13.388427839 and -13.388427839.Subproblem 1
x + -11.5 = 13.388427839 Simplifying x + -11.5 = 13.388427839 Reorder the terms: -11.5 + x = 13.388427839 Solving -11.5 + x = 13.388427839 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = 13.388427839 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 13.388427839 + 11.5 x = 13.388427839 + 11.5 Combine like terms: 13.388427839 + 11.5 = 24.888427839 x = 24.888427839 Simplifying x = 24.888427839Subproblem 2
x + -11.5 = -13.388427839 Simplifying x + -11.5 = -13.388427839 Reorder the terms: -11.5 + x = -13.388427839 Solving -11.5 + x = -13.388427839 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = -13.388427839 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -13.388427839 + 11.5 x = -13.388427839 + 11.5 Combine like terms: -13.388427839 + 11.5 = -1.888427839 x = -1.888427839 Simplifying x = -1.888427839Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.888427839, -1.888427839}
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