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Simplifying x2 + -76x + 1360 = 0 Reorder the terms: 1360 + -76x + x2 = 0 Solving 1360 + -76x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1360' to each side of the equation. 1360 + -76x + -1360 + x2 = 0 + -1360 Reorder the terms: 1360 + -1360 + -76x + x2 = 0 + -1360 Combine like terms: 1360 + -1360 = 0 0 + -76x + x2 = 0 + -1360 -76x + x2 = 0 + -1360 Combine like terms: 0 + -1360 = -1360 -76x + x2 = -1360 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 = -1360 + 1444 Reorder the terms: 1444 + -76x + x2 = -1360 + 1444 Combine like terms: -1360 + 1444 = 84 1444 + -76x + x2 = 84 Factor a perfect square on the left side: (x + -38)(x + -38) = 84 Calculate the square root of the right side: 9.16515139 Break this problem into two subproblems by setting (x + -38) equal to 9.16515139 and -9.16515139.Subproblem 1
x + -38 = 9.16515139 Simplifying x + -38 = 9.16515139 Reorder the terms: -38 + x = 9.16515139 Solving -38 + x = 9.16515139 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 = 9.16515139 + 38 Combine like terms: -38 + 38 = 0 0 + x = 9.16515139 + 38 x = 9.16515139 + 38 Combine like terms: 9.16515139 + 38 = 47.16515139 x = 47.16515139 Simplifying x = 47.16515139Subproblem 2
x + -38 = -9.16515139 Simplifying x + -38 = -9.16515139 Reorder the terms: -38 + x = -9.16515139 Solving -38 + x = -9.16515139 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 = -9.16515139 + 38 Combine like terms: -38 + 38 = 0 0 + x = -9.16515139 + 38 x = -9.16515139 + 38 Combine like terms: -9.16515139 + 38 = 28.83484861 x = 28.83484861 Simplifying x = 28.83484861Solution
The solution to the problem is based on the solutions from the subproblems. x = {47.16515139, 28.83484861}
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