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Simplifying x2 + 24x + -36 = 9 Reorder the terms: -36 + 24x + x2 = 9 Solving -36 + 24x + x2 = 9 Solving for variable 'x'. Reorder the terms: -36 + -9 + 24x + x2 = 9 + -9 Combine like terms: -36 + -9 = -45 -45 + 24x + x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -45 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + 24x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 24x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 24x + x2 = 0 + 45 24x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 24x + x2 = 45 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 = 45 + 144 Reorder the terms: 144 + 24x + x2 = 45 + 144 Combine like terms: 45 + 144 = 189 144 + 24x + x2 = 189 Factor a perfect square on the left side: (x + 12)(x + 12) = 189 Calculate the square root of the right side: 13.747727085 Break this problem into two subproblems by setting (x + 12) equal to 13.747727085 and -13.747727085.Subproblem 1
x + 12 = 13.747727085 Simplifying x + 12 = 13.747727085 Reorder the terms: 12 + x = 13.747727085 Solving 12 + x = 13.747727085 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 = 13.747727085 + -12 Combine like terms: 12 + -12 = 0 0 + x = 13.747727085 + -12 x = 13.747727085 + -12 Combine like terms: 13.747727085 + -12 = 1.747727085 x = 1.747727085 Simplifying x = 1.747727085Subproblem 2
x + 12 = -13.747727085 Simplifying x + 12 = -13.747727085 Reorder the terms: 12 + x = -13.747727085 Solving 12 + x = -13.747727085 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 = -13.747727085 + -12 Combine like terms: 12 + -12 = 0 0 + x = -13.747727085 + -12 x = -13.747727085 + -12 Combine like terms: -13.747727085 + -12 = -25.747727085 x = -25.747727085 Simplifying x = -25.747727085Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.747727085, -25.747727085}
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