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Simplifying x2 + 24x + 17 = 30 Reorder the terms: 17 + 24x + x2 = 30 Solving 17 + 24x + x2 = 30 Solving for variable 'x'. Reorder the terms: 17 + -30 + 24x + x2 = 30 + -30 Combine like terms: 17 + -30 = -13 -13 + 24x + x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -13 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 24x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 24x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 24x + x2 = 0 + 13 24x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 24x + x2 = 13 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 = 13 + 144 Reorder the terms: 144 + 24x + x2 = 13 + 144 Combine like terms: 13 + 144 = 157 144 + 24x + x2 = 157 Factor a perfect square on the left side: (x + 12)(x + 12) = 157 Calculate the square root of the right side: 12.529964086 Break this problem into two subproblems by setting (x + 12) equal to 12.529964086 and -12.529964086.Subproblem 1
x + 12 = 12.529964086 Simplifying x + 12 = 12.529964086 Reorder the terms: 12 + x = 12.529964086 Solving 12 + x = 12.529964086 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 = 12.529964086 + -12 Combine like terms: 12 + -12 = 0 0 + x = 12.529964086 + -12 x = 12.529964086 + -12 Combine like terms: 12.529964086 + -12 = 0.529964086 x = 0.529964086 Simplifying x = 0.529964086Subproblem 2
x + 12 = -12.529964086 Simplifying x + 12 = -12.529964086 Reorder the terms: 12 + x = -12.529964086 Solving 12 + x = -12.529964086 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 = -12.529964086 + -12 Combine like terms: 12 + -12 = 0 0 + x = -12.529964086 + -12 x = -12.529964086 + -12 Combine like terms: -12.529964086 + -12 = -24.529964086 x = -24.529964086 Simplifying x = -24.529964086Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.529964086, -24.529964086}
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