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Simplifying x2 + -26x + -48 = 0 Reorder the terms: -48 + -26x + x2 = 0 Solving -48 + -26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + -26x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + -26x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -26x + x2 = 0 + 48 -26x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 -26x + x2 = 48 The x term is -26x. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x + 169 + x2 = 48 + 169 Reorder the terms: 169 + -26x + x2 = 48 + 169 Combine like terms: 48 + 169 = 217 169 + -26x + x2 = 217 Factor a perfect square on the left side: (x + -13)(x + -13) = 217 Calculate the square root of the right side: 14.730919863 Break this problem into two subproblems by setting (x + -13) equal to 14.730919863 and -14.730919863.Subproblem 1
x + -13 = 14.730919863 Simplifying x + -13 = 14.730919863 Reorder the terms: -13 + x = 14.730919863 Solving -13 + x = 14.730919863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 14.730919863 + 13 Combine like terms: -13 + 13 = 0 0 + x = 14.730919863 + 13 x = 14.730919863 + 13 Combine like terms: 14.730919863 + 13 = 27.730919863 x = 27.730919863 Simplifying x = 27.730919863Subproblem 2
x + -13 = -14.730919863 Simplifying x + -13 = -14.730919863 Reorder the terms: -13 + x = -14.730919863 Solving -13 + x = -14.730919863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -14.730919863 + 13 Combine like terms: -13 + 13 = 0 0 + x = -14.730919863 + 13 x = -14.730919863 + 13 Combine like terms: -14.730919863 + 13 = -1.730919863 x = -1.730919863 Simplifying x = -1.730919863Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.730919863, -1.730919863}
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