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Simplifying 51x2 + -500x + 1000 = 0 Reorder the terms: 1000 + -500x + 51x2 = 0 Solving 1000 + -500x + 51x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 51 the coefficient of the squared term: Divide each side by '51'. 19.60784314 + -9.803921569x + x2 = 0 Move the constant term to the right: Add '-19.60784314' to each side of the equation. 19.60784314 + -9.803921569x + -19.60784314 + x2 = 0 + -19.60784314 Reorder the terms: 19.60784314 + -19.60784314 + -9.803921569x + x2 = 0 + -19.60784314 Combine like terms: 19.60784314 + -19.60784314 = 0.00000000 0.00000000 + -9.803921569x + x2 = 0 + -19.60784314 -9.803921569x + x2 = 0 + -19.60784314 Combine like terms: 0 + -19.60784314 = -19.60784314 -9.803921569x + x2 = -19.60784314 The x term is -9.803921569x. Take half its coefficient (-4.901960785). Square it (24.02921954) and add it to both sides. Add '24.02921954' to each side of the equation. -9.803921569x + 24.02921954 + x2 = -19.60784314 + 24.02921954 Reorder the terms: 24.02921954 + -9.803921569x + x2 = -19.60784314 + 24.02921954 Combine like terms: -19.60784314 + 24.02921954 = 4.4213764 24.02921954 + -9.803921569x + x2 = 4.4213764 Factor a perfect square on the left side: (x + -4.901960785)(x + -4.901960785) = 4.4213764 Calculate the square root of the right side: 2.102706922 Break this problem into two subproblems by setting (x + -4.901960785) equal to 2.102706922 and -2.102706922.Subproblem 1
x + -4.901960785 = 2.102706922 Simplifying x + -4.901960785 = 2.102706922 Reorder the terms: -4.901960785 + x = 2.102706922 Solving -4.901960785 + x = 2.102706922 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.901960785' to each side of the equation. -4.901960785 + 4.901960785 + x = 2.102706922 + 4.901960785 Combine like terms: -4.901960785 + 4.901960785 = 0.000000000 0.000000000 + x = 2.102706922 + 4.901960785 x = 2.102706922 + 4.901960785 Combine like terms: 2.102706922 + 4.901960785 = 7.004667707 x = 7.004667707 Simplifying x = 7.004667707Subproblem 2
x + -4.901960785 = -2.102706922 Simplifying x + -4.901960785 = -2.102706922 Reorder the terms: -4.901960785 + x = -2.102706922 Solving -4.901960785 + x = -2.102706922 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.901960785' to each side of the equation. -4.901960785 + 4.901960785 + x = -2.102706922 + 4.901960785 Combine like terms: -4.901960785 + 4.901960785 = 0.000000000 0.000000000 + x = -2.102706922 + 4.901960785 x = -2.102706922 + 4.901960785 Combine like terms: -2.102706922 + 4.901960785 = 2.799253863 x = 2.799253863 Simplifying x = 2.799253863Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.004667707, 2.799253863}
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