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Simplifying x2 + 47x + 12 = 0 Reorder the terms: 12 + 47x + x2 = 0 Solving 12 + 47x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 47x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + 47x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 47x + x2 = 0 + -12 47x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 47x + x2 = -12 The x term is 47x. Take half its coefficient (23.5). Square it (552.25) and add it to both sides. Add '552.25' to each side of the equation. 47x + 552.25 + x2 = -12 + 552.25 Reorder the terms: 552.25 + 47x + x2 = -12 + 552.25 Combine like terms: -12 + 552.25 = 540.25 552.25 + 47x + x2 = 540.25 Factor a perfect square on the left side: (x + 23.5)(x + 23.5) = 540.25 Calculate the square root of the right side: 23.243278598 Break this problem into two subproblems by setting (x + 23.5) equal to 23.243278598 and -23.243278598.Subproblem 1
x + 23.5 = 23.243278598 Simplifying x + 23.5 = 23.243278598 Reorder the terms: 23.5 + x = 23.243278598 Solving 23.5 + x = 23.243278598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23.5' to each side of the equation. 23.5 + -23.5 + x = 23.243278598 + -23.5 Combine like terms: 23.5 + -23.5 = 0.0 0.0 + x = 23.243278598 + -23.5 x = 23.243278598 + -23.5 Combine like terms: 23.243278598 + -23.5 = -0.256721402 x = -0.256721402 Simplifying x = -0.256721402Subproblem 2
x + 23.5 = -23.243278598 Simplifying x + 23.5 = -23.243278598 Reorder the terms: 23.5 + x = -23.243278598 Solving 23.5 + x = -23.243278598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23.5' to each side of the equation. 23.5 + -23.5 + x = -23.243278598 + -23.5 Combine like terms: 23.5 + -23.5 = 0.0 0.0 + x = -23.243278598 + -23.5 x = -23.243278598 + -23.5 Combine like terms: -23.243278598 + -23.5 = -46.743278598 x = -46.743278598 Simplifying x = -46.743278598Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.256721402, -46.743278598}
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