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Simplifying x2 + 13x + -9 = 12 Reorder the terms: -9 + 13x + x2 = 12 Solving -9 + 13x + x2 = 12 Solving for variable 'x'. Reorder the terms: -9 + -12 + 13x + x2 = 12 + -12 Combine like terms: -9 + -12 = -21 -21 + 13x + x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -21 + 13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + 13x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + 13x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 13x + x2 = 0 + 21 13x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 13x + x2 = 21 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 = 21 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 21 + 42.25 Combine like terms: 21 + 42.25 = 63.25 42.25 + 13x + x2 = 63.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 63.25 Calculate the square root of the right side: 7.95298686 Break this problem into two subproblems by setting (x + 6.5) equal to 7.95298686 and -7.95298686.Subproblem 1
x + 6.5 = 7.95298686 Simplifying x + 6.5 = 7.95298686 Reorder the terms: 6.5 + x = 7.95298686 Solving 6.5 + x = 7.95298686 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 = 7.95298686 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 7.95298686 + -6.5 x = 7.95298686 + -6.5 Combine like terms: 7.95298686 + -6.5 = 1.45298686 x = 1.45298686 Simplifying x = 1.45298686Subproblem 2
x + 6.5 = -7.95298686 Simplifying x + 6.5 = -7.95298686 Reorder the terms: 6.5 + x = -7.95298686 Solving 6.5 + x = -7.95298686 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 = -7.95298686 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -7.95298686 + -6.5 x = -7.95298686 + -6.5 Combine like terms: -7.95298686 + -6.5 = -14.45298686 x = -14.45298686 Simplifying x = -14.45298686Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.45298686, -14.45298686}
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