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Simplifying 13 + x(x + -13) + -1(2 + -5x) = 2.8 Reorder the terms: 13 + x(-13 + x) + -1(2 + -5x) = 2.8 13 + (-13 * x + x * x) + -1(2 + -5x) = 2.8 13 + (-13x + x2) + -1(2 + -5x) = 2.8 13 + -13x + x2 + (2 * -1 + -5x * -1) = 2.8 13 + -13x + x2 + (-2 + 5x) = 2.8 Reorder the terms: 13 + -2 + -13x + 5x + x2 = 2.8 Combine like terms: 13 + -2 = 11 11 + -13x + 5x + x2 = 2.8 Combine like terms: -13x + 5x = -8x 11 + -8x + x2 = 2.8 Solving 11 + -8x + x2 = 2.8 Solving for variable 'x'. Reorder the terms: 11 + -2.8 + -8x + x2 = 2.8 + -2.8 Combine like terms: 11 + -2.8 = 8.2 8.2 + -8x + x2 = 2.8 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 8.2 + -8x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '-8.2' to each side of the equation. 8.2 + -8x + -8.2 + x2 = 0.0 + -8.2 Reorder the terms: 8.2 + -8.2 + -8x + x2 = 0.0 + -8.2 Combine like terms: 8.2 + -8.2 = 0.0 0.0 + -8x + x2 = 0.0 + -8.2 -8x + x2 = 0.0 + -8.2 Combine like terms: 0.0 + -8.2 = -8.2 -8x + x2 = -8.2 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -8.2 + 16 Reorder the terms: 16 + -8x + x2 = -8.2 + 16 Combine like terms: -8.2 + 16 = 7.8 16 + -8x + x2 = 7.8 Factor a perfect square on the left side: (x + -4)(x + -4) = 7.8 Calculate the square root of the right side: 2.792848009 Break this problem into two subproblems by setting (x + -4) equal to 2.792848009 and -2.792848009.Subproblem 1
x + -4 = 2.792848009 Simplifying x + -4 = 2.792848009 Reorder the terms: -4 + x = 2.792848009 Solving -4 + x = 2.792848009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 2.792848009 + 4 Combine like terms: -4 + 4 = 0 0 + x = 2.792848009 + 4 x = 2.792848009 + 4 Combine like terms: 2.792848009 + 4 = 6.792848009 x = 6.792848009 Simplifying x = 6.792848009Subproblem 2
x + -4 = -2.792848009 Simplifying x + -4 = -2.792848009 Reorder the terms: -4 + x = -2.792848009 Solving -4 + x = -2.792848009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -2.792848009 + 4 Combine like terms: -4 + 4 = 0 0 + x = -2.792848009 + 4 x = -2.792848009 + 4 Combine like terms: -2.792848009 + 4 = 1.207151991 x = 1.207151991 Simplifying x = 1.207151991Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.792848009, 1.207151991}
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