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Simplifying x2 + -78x + -15 = 0 Reorder the terms: -15 + -78x + x2 = 0 Solving -15 + -78x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + -78x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -78x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -78x + x2 = 0 + 15 -78x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -78x + x2 = 15 The x term is -78x. Take half its coefficient (-39). Square it (1521) and add it to both sides. Add '1521' to each side of the equation. -78x + 1521 + x2 = 15 + 1521 Reorder the terms: 1521 + -78x + x2 = 15 + 1521 Combine like terms: 15 + 1521 = 1536 1521 + -78x + x2 = 1536 Factor a perfect square on the left side: (x + -39)(x + -39) = 1536 Calculate the square root of the right side: 39.191835885 Break this problem into two subproblems by setting (x + -39) equal to 39.191835885 and -39.191835885.Subproblem 1
x + -39 = 39.191835885 Simplifying x + -39 = 39.191835885 Reorder the terms: -39 + x = 39.191835885 Solving -39 + x = 39.191835885 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '39' to each side of the equation. -39 + 39 + x = 39.191835885 + 39 Combine like terms: -39 + 39 = 0 0 + x = 39.191835885 + 39 x = 39.191835885 + 39 Combine like terms: 39.191835885 + 39 = 78.191835885 x = 78.191835885 Simplifying x = 78.191835885Subproblem 2
x + -39 = -39.191835885 Simplifying x + -39 = -39.191835885 Reorder the terms: -39 + x = -39.191835885 Solving -39 + x = -39.191835885 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '39' to each side of the equation. -39 + 39 + x = -39.191835885 + 39 Combine like terms: -39 + 39 = 0 0 + x = -39.191835885 + 39 x = -39.191835885 + 39 Combine like terms: -39.191835885 + 39 = -0.191835885 x = -0.191835885 Simplifying x = -0.191835885Solution
The solution to the problem is based on the solutions from the subproblems. x = {78.191835885, -0.191835885}
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