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Simplifying x2 + 46x + -28 = 0 Reorder the terms: -28 + 46x + x2 = 0 Solving -28 + 46x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + 46x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + 46x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 46x + x2 = 0 + 28 46x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 46x + x2 = 28 The x term is 46x. Take half its coefficient (23). Square it (529) and add it to both sides. Add '529' to each side of the equation. 46x + 529 + x2 = 28 + 529 Reorder the terms: 529 + 46x + x2 = 28 + 529 Combine like terms: 28 + 529 = 557 529 + 46x + x2 = 557 Factor a perfect square on the left side: (x + 23)(x + 23) = 557 Calculate the square root of the right side: 23.600847442 Break this problem into two subproblems by setting (x + 23) equal to 23.600847442 and -23.600847442.Subproblem 1
x + 23 = 23.600847442 Simplifying x + 23 = 23.600847442 Reorder the terms: 23 + x = 23.600847442 Solving 23 + x = 23.600847442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + x = 23.600847442 + -23 Combine like terms: 23 + -23 = 0 0 + x = 23.600847442 + -23 x = 23.600847442 + -23 Combine like terms: 23.600847442 + -23 = 0.600847442 x = 0.600847442 Simplifying x = 0.600847442Subproblem 2
x + 23 = -23.600847442 Simplifying x + 23 = -23.600847442 Reorder the terms: 23 + x = -23.600847442 Solving 23 + x = -23.600847442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + x = -23.600847442 + -23 Combine like terms: 23 + -23 = 0 0 + x = -23.600847442 + -23 x = -23.600847442 + -23 Combine like terms: -23.600847442 + -23 = -46.600847442 x = -46.600847442 Simplifying x = -46.600847442Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.600847442, -46.600847442}
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