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Simplifying x2 + -8x + -48 = -6 Reorder the terms: -48 + -8x + x2 = -6 Solving -48 + -8x + x2 = -6 Solving for variable 'x'. Reorder the terms: -48 + 6 + -8x + x2 = -6 + 6 Combine like terms: -48 + 6 = -42 -42 + -8x + x2 = -6 + 6 Combine like terms: -6 + 6 = 0 -42 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + -8x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + -8x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -8x + x2 = 0 + 42 -8x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 -8x + x2 = 42 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 = 42 + 16 Reorder the terms: 16 + -8x + x2 = 42 + 16 Combine like terms: 42 + 16 = 58 16 + -8x + x2 = 58 Factor a perfect square on the left side: (x + -4)(x + -4) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (x + -4) equal to 7.615773106 and -7.615773106.Subproblem 1
x + -4 = 7.615773106 Simplifying x + -4 = 7.615773106 Reorder the terms: -4 + x = 7.615773106 Solving -4 + x = 7.615773106 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 = 7.615773106 + 4 Combine like terms: -4 + 4 = 0 0 + x = 7.615773106 + 4 x = 7.615773106 + 4 Combine like terms: 7.615773106 + 4 = 11.615773106 x = 11.615773106 Simplifying x = 11.615773106Subproblem 2
x + -4 = -7.615773106 Simplifying x + -4 = -7.615773106 Reorder the terms: -4 + x = -7.615773106 Solving -4 + x = -7.615773106 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 = -7.615773106 + 4 Combine like terms: -4 + 4 = 0 0 + x = -7.615773106 + 4 x = -7.615773106 + 4 Combine like terms: -7.615773106 + 4 = -3.615773106 x = -3.615773106 Simplifying x = -3.615773106Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.615773106, -3.615773106}
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