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Simplifying x2 + -76x + -7600 = 0 Reorder the terms: -7600 + -76x + x2 = 0 Solving -7600 + -76x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '7600' to each side of the equation. -7600 + -76x + 7600 + x2 = 0 + 7600 Reorder the terms: -7600 + 7600 + -76x + x2 = 0 + 7600 Combine like terms: -7600 + 7600 = 0 0 + -76x + x2 = 0 + 7600 -76x + x2 = 0 + 7600 Combine like terms: 0 + 7600 = 7600 -76x + x2 = 7600 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 = 7600 + 1444 Reorder the terms: 1444 + -76x + x2 = 7600 + 1444 Combine like terms: 7600 + 1444 = 9044 1444 + -76x + x2 = 9044 Factor a perfect square on the left side: (x + -38)(x + -38) = 9044 Calculate the square root of the right side: 95.099947424 Break this problem into two subproblems by setting (x + -38) equal to 95.099947424 and -95.099947424.Subproblem 1
x + -38 = 95.099947424 Simplifying x + -38 = 95.099947424 Reorder the terms: -38 + x = 95.099947424 Solving -38 + x = 95.099947424 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 = 95.099947424 + 38 Combine like terms: -38 + 38 = 0 0 + x = 95.099947424 + 38 x = 95.099947424 + 38 Combine like terms: 95.099947424 + 38 = 133.099947424 x = 133.099947424 Simplifying x = 133.099947424Subproblem 2
x + -38 = -95.099947424 Simplifying x + -38 = -95.099947424 Reorder the terms: -38 + x = -95.099947424 Solving -38 + x = -95.099947424 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 = -95.099947424 + 38 Combine like terms: -38 + 38 = 0 0 + x = -95.099947424 + 38 x = -95.099947424 + 38 Combine like terms: -95.099947424 + 38 = -57.099947424 x = -57.099947424 Simplifying x = -57.099947424Solution
The solution to the problem is based on the solutions from the subproblems. x = {133.099947424, -57.099947424}
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