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Simplifying x2 + 140x + 1275 = 0 Reorder the terms: 1275 + 140x + x2 = 0 Solving 1275 + 140x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1275' to each side of the equation. 1275 + 140x + -1275 + x2 = 0 + -1275 Reorder the terms: 1275 + -1275 + 140x + x2 = 0 + -1275 Combine like terms: 1275 + -1275 = 0 0 + 140x + x2 = 0 + -1275 140x + x2 = 0 + -1275 Combine like terms: 0 + -1275 = -1275 140x + x2 = -1275 The x term is 140x. Take half its coefficient (70). Square it (4900) and add it to both sides. Add '4900' to each side of the equation. 140x + 4900 + x2 = -1275 + 4900 Reorder the terms: 4900 + 140x + x2 = -1275 + 4900 Combine like terms: -1275 + 4900 = 3625 4900 + 140x + x2 = 3625 Factor a perfect square on the left side: (x + 70)(x + 70) = 3625 Calculate the square root of the right side: 60.207972894 Break this problem into two subproblems by setting (x + 70) equal to 60.207972894 and -60.207972894.Subproblem 1
x + 70 = 60.207972894 Simplifying x + 70 = 60.207972894 Reorder the terms: 70 + x = 60.207972894 Solving 70 + x = 60.207972894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-70' to each side of the equation. 70 + -70 + x = 60.207972894 + -70 Combine like terms: 70 + -70 = 0 0 + x = 60.207972894 + -70 x = 60.207972894 + -70 Combine like terms: 60.207972894 + -70 = -9.792027106 x = -9.792027106 Simplifying x = -9.792027106Subproblem 2
x + 70 = -60.207972894 Simplifying x + 70 = -60.207972894 Reorder the terms: 70 + x = -60.207972894 Solving 70 + x = -60.207972894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-70' to each side of the equation. 70 + -70 + x = -60.207972894 + -70 Combine like terms: 70 + -70 = 0 0 + x = -60.207972894 + -70 x = -60.207972894 + -70 Combine like terms: -60.207972894 + -70 = -130.207972894 x = -130.207972894 Simplifying x = -130.207972894Solution
The solution to the problem is based on the solutions from the subproblems. x = {-9.792027106, -130.207972894}
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