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Simplifying x2 + -47x + 448 = 0 Reorder the terms: 448 + -47x + x2 = 0 Solving 448 + -47x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-448' to each side of the equation. 448 + -47x + -448 + x2 = 0 + -448 Reorder the terms: 448 + -448 + -47x + x2 = 0 + -448 Combine like terms: 448 + -448 = 0 0 + -47x + x2 = 0 + -448 -47x + x2 = 0 + -448 Combine like terms: 0 + -448 = -448 -47x + x2 = -448 The x term is -47x. Take half its coefficient (-23.5). Square it (552.25) and add it to both sides. Add '552.25' to each side of the equation. -47x + 552.25 + x2 = -448 + 552.25 Reorder the terms: 552.25 + -47x + x2 = -448 + 552.25 Combine like terms: -448 + 552.25 = 104.25 552.25 + -47x + x2 = 104.25 Factor a perfect square on the left side: (x + -23.5)(x + -23.5) = 104.25 Calculate the square root of the right side: 10.210288928 Break this problem into two subproblems by setting (x + -23.5) equal to 10.210288928 and -10.210288928.Subproblem 1
x + -23.5 = 10.210288928 Simplifying x + -23.5 = 10.210288928 Reorder the terms: -23.5 + x = 10.210288928 Solving -23.5 + x = 10.210288928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23.5' to each side of the equation. -23.5 + 23.5 + x = 10.210288928 + 23.5 Combine like terms: -23.5 + 23.5 = 0.0 0.0 + x = 10.210288928 + 23.5 x = 10.210288928 + 23.5 Combine like terms: 10.210288928 + 23.5 = 33.710288928 x = 33.710288928 Simplifying x = 33.710288928Subproblem 2
x + -23.5 = -10.210288928 Simplifying x + -23.5 = -10.210288928 Reorder the terms: -23.5 + x = -10.210288928 Solving -23.5 + x = -10.210288928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23.5' to each side of the equation. -23.5 + 23.5 + x = -10.210288928 + 23.5 Combine like terms: -23.5 + 23.5 = 0.0 0.0 + x = -10.210288928 + 23.5 x = -10.210288928 + 23.5 Combine like terms: -10.210288928 + 23.5 = 13.289711072 x = 13.289711072 Simplifying x = 13.289711072Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.710288928, 13.289711072}
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