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Simplifying x2 + -43x + -18 = 0 Reorder the terms: -18 + -43x + x2 = 0 Solving -18 + -43x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -43x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -43x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -43x + x2 = 0 + 18 -43x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -43x + x2 = 18 The x term is -43x. Take half its coefficient (-21.5). Square it (462.25) and add it to both sides. Add '462.25' to each side of the equation. -43x + 462.25 + x2 = 18 + 462.25 Reorder the terms: 462.25 + -43x + x2 = 18 + 462.25 Combine like terms: 18 + 462.25 = 480.25 462.25 + -43x + x2 = 480.25 Factor a perfect square on the left side: (x + -21.5)(x + -21.5) = 480.25 Calculate the square root of the right side: 21.914607001 Break this problem into two subproblems by setting (x + -21.5) equal to 21.914607001 and -21.914607001.Subproblem 1
x + -21.5 = 21.914607001 Simplifying x + -21.5 = 21.914607001 Reorder the terms: -21.5 + x = 21.914607001 Solving -21.5 + x = 21.914607001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21.5' to each side of the equation. -21.5 + 21.5 + x = 21.914607001 + 21.5 Combine like terms: -21.5 + 21.5 = 0.0 0.0 + x = 21.914607001 + 21.5 x = 21.914607001 + 21.5 Combine like terms: 21.914607001 + 21.5 = 43.414607001 x = 43.414607001 Simplifying x = 43.414607001Subproblem 2
x + -21.5 = -21.914607001 Simplifying x + -21.5 = -21.914607001 Reorder the terms: -21.5 + x = -21.914607001 Solving -21.5 + x = -21.914607001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21.5' to each side of the equation. -21.5 + 21.5 + x = -21.914607001 + 21.5 Combine like terms: -21.5 + 21.5 = 0.0 0.0 + x = -21.914607001 + 21.5 x = -21.914607001 + 21.5 Combine like terms: -21.914607001 + 21.5 = -0.414607001 x = -0.414607001 Simplifying x = -0.414607001Solution
The solution to the problem is based on the solutions from the subproblems. x = {43.414607001, -0.414607001}
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