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Simplifying 32 = x2 + -13x Reorder the terms: 32 = -13x + x2 Solving 32 = -13x + x2 Solving for variable 'x'. Reorder the terms: 32 + 13x + -1x2 = -13x + 13x + x2 + -1x2 Combine like terms: -13x + 13x = 0 32 + 13x + -1x2 = 0 + x2 + -1x2 32 + 13x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 32 + 13x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -32 + -13x + x2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + -13x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + -13x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -13x + x2 = 0 + 32 -13x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 -13x + x2 = 32 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = 32 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 32 + 42.25 Combine like terms: 32 + 42.25 = 74.25 42.25 + -13x + x2 = 74.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 74.25 Calculate the square root of the right side: 8.61684397 Break this problem into two subproblems by setting (x + -6.5) equal to 8.61684397 and -8.61684397.Subproblem 1
x + -6.5 = 8.61684397 Simplifying x + -6.5 = 8.61684397 Reorder the terms: -6.5 + x = 8.61684397 Solving -6.5 + x = 8.61684397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 8.61684397 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 8.61684397 + 6.5 x = 8.61684397 + 6.5 Combine like terms: 8.61684397 + 6.5 = 15.11684397 x = 15.11684397 Simplifying x = 15.11684397Subproblem 2
x + -6.5 = -8.61684397 Simplifying x + -6.5 = -8.61684397 Reorder the terms: -6.5 + x = -8.61684397 Solving -6.5 + x = -8.61684397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -8.61684397 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -8.61684397 + 6.5 x = -8.61684397 + 6.5 Combine like terms: -8.61684397 + 6.5 = -2.11684397 x = -2.11684397 Simplifying x = -2.11684397Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.11684397, -2.11684397}
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