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Simplifying (24 + x) * x = 84 Reorder the terms for easier multiplication: x(24 + x) = 84 (24 * x + x * x) = 84 (24x + x2) = 84 Solving 24x + x2 = 84 Solving for variable 'x'. Reorder the terms: -84 + 24x + x2 = 84 + -84 Combine like terms: 84 + -84 = 0 -84 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '84' to each side of the equation. -84 + 24x + 84 + x2 = 0 + 84 Reorder the terms: -84 + 84 + 24x + x2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + 24x + x2 = 0 + 84 24x + x2 = 0 + 84 Combine like terms: 0 + 84 = 84 24x + x2 = 84 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 = 84 + 144 Reorder the terms: 144 + 24x + x2 = 84 + 144 Combine like terms: 84 + 144 = 228 144 + 24x + x2 = 228 Factor a perfect square on the left side: (x + 12)(x + 12) = 228 Calculate the square root of the right side: 15.099668871 Break this problem into two subproblems by setting (x + 12) equal to 15.099668871 and -15.099668871.Subproblem 1
x + 12 = 15.099668871 Simplifying x + 12 = 15.099668871 Reorder the terms: 12 + x = 15.099668871 Solving 12 + x = 15.099668871 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 = 15.099668871 + -12 Combine like terms: 12 + -12 = 0 0 + x = 15.099668871 + -12 x = 15.099668871 + -12 Combine like terms: 15.099668871 + -12 = 3.099668871 x = 3.099668871 Simplifying x = 3.099668871Subproblem 2
x + 12 = -15.099668871 Simplifying x + 12 = -15.099668871 Reorder the terms: 12 + x = -15.099668871 Solving 12 + x = -15.099668871 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 = -15.099668871 + -12 Combine like terms: 12 + -12 = 0 0 + x = -15.099668871 + -12 x = -15.099668871 + -12 Combine like terms: -15.099668871 + -12 = -27.099668871 x = -27.099668871 Simplifying x = -27.099668871Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.099668871, -27.099668871}
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