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Simplifying x2 + -24x + 48 = -48 Reorder the terms: 48 + -24x + x2 = -48 Solving 48 + -24x + x2 = -48 Solving for variable 'x'. Reorder the terms: 48 + 48 + -24x + x2 = -48 + 48 Combine like terms: 48 + 48 = 96 96 + -24x + x2 = -48 + 48 Combine like terms: -48 + 48 = 0 96 + -24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-96' to each side of the equation. 96 + -24x + -96 + x2 = 0 + -96 Reorder the terms: 96 + -96 + -24x + x2 = 0 + -96 Combine like terms: 96 + -96 = 0 0 + -24x + x2 = 0 + -96 -24x + x2 = 0 + -96 Combine like terms: 0 + -96 = -96 -24x + x2 = -96 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = -96 + 144 Reorder the terms: 144 + -24x + x2 = -96 + 144 Combine like terms: -96 + 144 = 48 144 + -24x + x2 = 48 Factor a perfect square on the left side: (x + -12)(x + -12) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (x + -12) equal to 6.92820323 and -6.92820323.Subproblem 1
x + -12 = 6.92820323 Simplifying x + -12 = 6.92820323 Reorder the terms: -12 + x = 6.92820323 Solving -12 + x = 6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 6.92820323 + 12 Combine like terms: -12 + 12 = 0 0 + x = 6.92820323 + 12 x = 6.92820323 + 12 Combine like terms: 6.92820323 + 12 = 18.92820323 x = 18.92820323 Simplifying x = 18.92820323Subproblem 2
x + -12 = -6.92820323 Simplifying x + -12 = -6.92820323 Reorder the terms: -12 + x = -6.92820323 Solving -12 + x = -6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -6.92820323 + 12 Combine like terms: -12 + 12 = 0 0 + x = -6.92820323 + 12 x = -6.92820323 + 12 Combine like terms: -6.92820323 + 12 = 5.07179677 x = 5.07179677 Simplifying x = 5.07179677Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.92820323, 5.07179677}
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