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Simplifying x2 + -76x + 1300 + -196 = 0 Reorder the terms: 1300 + -196 + -76x + x2 = 0 Combine like terms: 1300 + -196 = 1104 1104 + -76x + x2 = 0 Solving 1104 + -76x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1104' to each side of the equation. 1104 + -76x + -1104 + x2 = 0 + -1104 Reorder the terms: 1104 + -1104 + -76x + x2 = 0 + -1104 Combine like terms: 1104 + -1104 = 0 0 + -76x + x2 = 0 + -1104 -76x + x2 = 0 + -1104 Combine like terms: 0 + -1104 = -1104 -76x + x2 = -1104 The x term is -76x. Take half its coefficient (-38). Square it (1444) and add it to both sides. Add '1444' to each side of the equation. -76x + 1444 + x2 = -1104 + 1444 Reorder the terms: 1444 + -76x + x2 = -1104 + 1444 Combine like terms: -1104 + 1444 = 340 1444 + -76x + x2 = 340 Factor a perfect square on the left side: (x + -38)(x + -38) = 340 Calculate the square root of the right side: 18.439088915 Break this problem into two subproblems by setting (x + -38) equal to 18.439088915 and -18.439088915.Subproblem 1
x + -38 = 18.439088915 Simplifying x + -38 = 18.439088915 Reorder the terms: -38 + x = 18.439088915 Solving -38 + x = 18.439088915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '38' to each side of the equation. -38 + 38 + x = 18.439088915 + 38 Combine like terms: -38 + 38 = 0 0 + x = 18.439088915 + 38 x = 18.439088915 + 38 Combine like terms: 18.439088915 + 38 = 56.439088915 x = 56.439088915 Simplifying x = 56.439088915Subproblem 2
x + -38 = -18.439088915 Simplifying x + -38 = -18.439088915 Reorder the terms: -38 + x = -18.439088915 Solving -38 + x = -18.439088915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '38' to each side of the equation. -38 + 38 + x = -18.439088915 + 38 Combine like terms: -38 + 38 = 0 0 + x = -18.439088915 + 38 x = -18.439088915 + 38 Combine like terms: -18.439088915 + 38 = 19.560911085 x = 19.560911085 Simplifying x = 19.560911085Solution
The solution to the problem is based on the solutions from the subproblems. x = {56.439088915, 19.560911085}
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