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Simplifying x2 = 13x + -32 Reorder the terms: x2 = -32 + 13x Solving x2 = -32 + 13x Solving for variable 'x'. Reorder the terms: 32 + -13x + x2 = -32 + 13x + 32 + -13x Reorder the terms: 32 + -13x + x2 = -32 + 32 + 13x + -13x Combine like terms: -32 + 32 = 0 32 + -13x + x2 = 0 + 13x + -13x 32 + -13x + x2 = 13x + -13x Combine like terms: 13x + -13x = 0 32 + -13x + x2 = 0 Begin completing the square. 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 = 10.25 42.25 + -13x + x2 = 10.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (x + -6.5) equal to 3.201562119 and -3.201562119.Subproblem 1
x + -6.5 = 3.201562119 Simplifying x + -6.5 = 3.201562119 Reorder the terms: -6.5 + x = 3.201562119 Solving -6.5 + x = 3.201562119 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 = 3.201562119 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 3.201562119 + 6.5 x = 3.201562119 + 6.5 Combine like terms: 3.201562119 + 6.5 = 9.701562119 x = 9.701562119 Simplifying x = 9.701562119Subproblem 2
x + -6.5 = -3.201562119 Simplifying x + -6.5 = -3.201562119 Reorder the terms: -6.5 + x = -3.201562119 Solving -6.5 + x = -3.201562119 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 = -3.201562119 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -3.201562119 + 6.5 x = -3.201562119 + 6.5 Combine like terms: -3.201562119 + 6.5 = 3.298437881 x = 3.298437881 Simplifying x = 3.298437881Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.701562119, 3.298437881}
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