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Simplifying x2 + 46x + -4 = 0 Reorder the terms: -4 + 46x + x2 = 0 Solving -4 + 46x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 46x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 46x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 46x + x2 = 0 + 4 46x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 46x + x2 = 4 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 = 4 + 529 Reorder the terms: 529 + 46x + x2 = 4 + 529 Combine like terms: 4 + 529 = 533 529 + 46x + x2 = 533 Factor a perfect square on the left side: (x + 23)(x + 23) = 533 Calculate the square root of the right side: 23.086792761 Break this problem into two subproblems by setting (x + 23) equal to 23.086792761 and -23.086792761.Subproblem 1
x + 23 = 23.086792761 Simplifying x + 23 = 23.086792761 Reorder the terms: 23 + x = 23.086792761 Solving 23 + x = 23.086792761 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 = 23.086792761 + -23 Combine like terms: 23 + -23 = 0 0 + x = 23.086792761 + -23 x = 23.086792761 + -23 Combine like terms: 23.086792761 + -23 = 0.086792761 x = 0.086792761 Simplifying x = 0.086792761Subproblem 2
x + 23 = -23.086792761 Simplifying x + 23 = -23.086792761 Reorder the terms: 23 + x = -23.086792761 Solving 23 + x = -23.086792761 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 = -23.086792761 + -23 Combine like terms: 23 + -23 = 0 0 + x = -23.086792761 + -23 x = -23.086792761 + -23 Combine like terms: -23.086792761 + -23 = -46.086792761 x = -46.086792761 Simplifying x = -46.086792761Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.086792761, -46.086792761}
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