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Simplifying 400 = x * x + (x + -6) Multiply x * x 400 = x2 + (x + -6) Reorder the terms: 400 = x2 + (-6 + x) Remove parenthesis around (-6 + x) 400 = x2 + -6 + x Reorder the terms: 400 = -6 + x + x2 Solving 400 = -6 + x + x2 Solving for variable 'x'. Combine like terms: 400 + 6 = 406 406 + -1x + -1x2 = -6 + x + x2 + 6 + -1x + -1x2 Reorder the terms: 406 + -1x + -1x2 = -6 + 6 + x + -1x + x2 + -1x2 Combine like terms: -6 + 6 = 0 406 + -1x + -1x2 = 0 + x + -1x + x2 + -1x2 406 + -1x + -1x2 = x + -1x + x2 + -1x2 Combine like terms: x + -1x = 0 406 + -1x + -1x2 = 0 + x2 + -1x2 406 + -1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 406 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -406 + x + x2 = 0 Move the constant term to the right: Add '406' to each side of the equation. -406 + x + 406 + x2 = 0 + 406 Reorder the terms: -406 + 406 + x + x2 = 0 + 406 Combine like terms: -406 + 406 = 0 0 + x + x2 = 0 + 406 x + x2 = 0 + 406 Combine like terms: 0 + 406 = 406 x + x2 = 406 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 406 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 406 + 0.25 Combine like terms: 406 + 0.25 = 406.25 1.25 + x2 = 406.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 406.25 Calculate the square root of the right side: 20.155644371 Break this problem into two subproblems by setting (x + 0.5) equal to 20.155644371 and -20.155644371.Subproblem 1
x + 0.5 = 20.155644371 Simplifying x + 0.5 = 20.155644371 Reorder the terms: 0.5 + x = 20.155644371 Solving 0.5 + x = 20.155644371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 20.155644371 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 20.155644371 + -0.5 x = 20.155644371 + -0.5 Combine like terms: 20.155644371 + -0.5 = 19.655644371 x = 19.655644371 Simplifying x = 19.655644371Subproblem 2
x + 0.5 = -20.155644371 Simplifying x + 0.5 = -20.155644371 Reorder the terms: 0.5 + x = -20.155644371 Solving 0.5 + x = -20.155644371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -20.155644371 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -20.155644371 + -0.5 x = -20.155644371 + -0.5 Combine like terms: -20.155644371 + -0.5 = -20.655644371 x = -20.655644371 Simplifying x = -20.655644371Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.655644371, -20.655644371}
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