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Simplifying (x)(x) = 13x + -28 Multiply x * x x2 = 13x + -28 Reorder the terms: x2 = -28 + 13x Solving x2 = -28 + 13x Solving for variable 'x'. Reorder the terms: 28 + -13x + x2 = -28 + 13x + 28 + -13x Reorder the terms: 28 + -13x + x2 = -28 + 28 + 13x + -13x Combine like terms: -28 + 28 = 0 28 + -13x + x2 = 0 + 13x + -13x 28 + -13x + x2 = 13x + -13x Combine like terms: 13x + -13x = 0 28 + -13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-28' to each side of the equation. 28 + -13x + -28 + x2 = 0 + -28 Reorder the terms: 28 + -28 + -13x + x2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -13x + x2 = 0 + -28 -13x + x2 = 0 + -28 Combine like terms: 0 + -28 = -28 -13x + x2 = -28 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 = -28 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -28 + 42.25 Combine like terms: -28 + 42.25 = 14.25 42.25 + -13x + x2 = 14.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (x + -6.5) equal to 3.774917218 and -3.774917218.Subproblem 1
x + -6.5 = 3.774917218 Simplifying x + -6.5 = 3.774917218 Reorder the terms: -6.5 + x = 3.774917218 Solving -6.5 + x = 3.774917218 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 = 3.774917218 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 3.774917218 + 6.5 x = 3.774917218 + 6.5 Combine like terms: 3.774917218 + 6.5 = 10.274917218 x = 10.274917218 Simplifying x = 10.274917218Subproblem 2
x + -6.5 = -3.774917218 Simplifying x + -6.5 = -3.774917218 Reorder the terms: -6.5 + x = -3.774917218 Solving -6.5 + x = -3.774917218 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 = -3.774917218 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -3.774917218 + 6.5 x = -3.774917218 + 6.5 Combine like terms: -3.774917218 + 6.5 = 2.725082782 x = 2.725082782 Simplifying x = 2.725082782Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.274917218, 2.725082782}
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