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Simplifying x2 + 300x + -58 = 0 Reorder the terms: -58 + 300x + x2 = 0 Solving -58 + 300x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '58' to each side of the equation. -58 + 300x + 58 + x2 = 0 + 58 Reorder the terms: -58 + 58 + 300x + x2 = 0 + 58 Combine like terms: -58 + 58 = 0 0 + 300x + x2 = 0 + 58 300x + x2 = 0 + 58 Combine like terms: 0 + 58 = 58 300x + x2 = 58 The x term is 300x. Take half its coefficient (150). Square it (22500) and add it to both sides. Add '22500' to each side of the equation. 300x + 22500 + x2 = 58 + 22500 Reorder the terms: 22500 + 300x + x2 = 58 + 22500 Combine like terms: 58 + 22500 = 22558 22500 + 300x + x2 = 22558 Factor a perfect square on the left side: (x + 150)(x + 150) = 22558 Calculate the square root of the right side: 150.193208901 Break this problem into two subproblems by setting (x + 150) equal to 150.193208901 and -150.193208901.Subproblem 1
x + 150 = 150.193208901 Simplifying x + 150 = 150.193208901 Reorder the terms: 150 + x = 150.193208901 Solving 150 + x = 150.193208901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-150' to each side of the equation. 150 + -150 + x = 150.193208901 + -150 Combine like terms: 150 + -150 = 0 0 + x = 150.193208901 + -150 x = 150.193208901 + -150 Combine like terms: 150.193208901 + -150 = 0.193208901 x = 0.193208901 Simplifying x = 0.193208901Subproblem 2
x + 150 = -150.193208901 Simplifying x + 150 = -150.193208901 Reorder the terms: 150 + x = -150.193208901 Solving 150 + x = -150.193208901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-150' to each side of the equation. 150 + -150 + x = -150.193208901 + -150 Combine like terms: 150 + -150 = 0 0 + x = -150.193208901 + -150 x = -150.193208901 + -150 Combine like terms: -150.193208901 + -150 = -300.193208901 x = -300.193208901 Simplifying x = -300.193208901Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.193208901, -300.193208901}
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