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Simplifying x2 + 15x + -38 = 0 Reorder the terms: -38 + 15x + x2 = 0 Solving -38 + 15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + 15x + 38 + x2 = 0 + 38 Reorder the terms: -38 + 38 + 15x + x2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + 15x + x2 = 0 + 38 15x + x2 = 0 + 38 Combine like terms: 0 + 38 = 38 15x + x2 = 38 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 38 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 38 + 56.25 Combine like terms: 38 + 56.25 = 94.25 56.25 + 15x + x2 = 94.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 94.25 Calculate the square root of the right side: 9.708243919 Break this problem into two subproblems by setting (x + 7.5) equal to 9.708243919 and -9.708243919.Subproblem 1
x + 7.5 = 9.708243919 Simplifying x + 7.5 = 9.708243919 Reorder the terms: 7.5 + x = 9.708243919 Solving 7.5 + x = 9.708243919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 9.708243919 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 9.708243919 + -7.5 x = 9.708243919 + -7.5 Combine like terms: 9.708243919 + -7.5 = 2.208243919 x = 2.208243919 Simplifying x = 2.208243919Subproblem 2
x + 7.5 = -9.708243919 Simplifying x + 7.5 = -9.708243919 Reorder the terms: 7.5 + x = -9.708243919 Solving 7.5 + x = -9.708243919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -9.708243919 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -9.708243919 + -7.5 x = -9.708243919 + -7.5 Combine like terms: -9.708243919 + -7.5 = -17.208243919 x = -17.208243919 Simplifying x = -17.208243919Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.208243919, -17.208243919}
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