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Simplifying x2 + 7x + -23 = 0 Reorder the terms: -23 + 7x + x2 = 0 Solving -23 + 7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + 7x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + 7x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 7x + x2 = 0 + 23 7x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 7x + x2 = 23 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 23 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 23 + 12.25 Combine like terms: 23 + 12.25 = 35.25 12.25 + 7x + x2 = 35.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 35.25 Calculate the square root of the right side: 5.937171044 Break this problem into two subproblems by setting (x + 3.5) equal to 5.937171044 and -5.937171044.Subproblem 1
x + 3.5 = 5.937171044 Simplifying x + 3.5 = 5.937171044 Reorder the terms: 3.5 + x = 5.937171044 Solving 3.5 + x = 5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 5.937171044 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 5.937171044 + -3.5 x = 5.937171044 + -3.5 Combine like terms: 5.937171044 + -3.5 = 2.437171044 x = 2.437171044 Simplifying x = 2.437171044Subproblem 2
x + 3.5 = -5.937171044 Simplifying x + 3.5 = -5.937171044 Reorder the terms: 3.5 + x = -5.937171044 Solving 3.5 + x = -5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -5.937171044 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -5.937171044 + -3.5 x = -5.937171044 + -3.5 Combine like terms: -5.937171044 + -3.5 = -9.437171044 x = -9.437171044 Simplifying x = -9.437171044Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.437171044, -9.437171044}
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