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Simplifying x2 + 58x + -3480 = 0 Reorder the terms: -3480 + 58x + x2 = 0 Solving -3480 + 58x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3480' to each side of the equation. -3480 + 58x + 3480 + x2 = 0 + 3480 Reorder the terms: -3480 + 3480 + 58x + x2 = 0 + 3480 Combine like terms: -3480 + 3480 = 0 0 + 58x + x2 = 0 + 3480 58x + x2 = 0 + 3480 Combine like terms: 0 + 3480 = 3480 58x + x2 = 3480 The x term is 58x. Take half its coefficient (29). Square it (841) and add it to both sides. Add '841' to each side of the equation. 58x + 841 + x2 = 3480 + 841 Reorder the terms: 841 + 58x + x2 = 3480 + 841 Combine like terms: 3480 + 841 = 4321 841 + 58x + x2 = 4321 Factor a perfect square on the left side: (x + 29)(x + 29) = 4321 Calculate the square root of the right side: 65.734313718 Break this problem into two subproblems by setting (x + 29) equal to 65.734313718 and -65.734313718.Subproblem 1
x + 29 = 65.734313718 Simplifying x + 29 = 65.734313718 Reorder the terms: 29 + x = 65.734313718 Solving 29 + x = 65.734313718 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + x = 65.734313718 + -29 Combine like terms: 29 + -29 = 0 0 + x = 65.734313718 + -29 x = 65.734313718 + -29 Combine like terms: 65.734313718 + -29 = 36.734313718 x = 36.734313718 Simplifying x = 36.734313718Subproblem 2
x + 29 = -65.734313718 Simplifying x + 29 = -65.734313718 Reorder the terms: 29 + x = -65.734313718 Solving 29 + x = -65.734313718 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + x = -65.734313718 + -29 Combine like terms: 29 + -29 = 0 0 + x = -65.734313718 + -29 x = -65.734313718 + -29 Combine like terms: -65.734313718 + -29 = -94.734313718 x = -94.734313718 Simplifying x = -94.734313718Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.734313718, -94.734313718}
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