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Simplifying 24x + x2 = 24 Solving 24x + x2 = 24 Solving for variable 'x'. Reorder the terms: -24 + 24x + x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + 24x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 24x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 24x + x2 = 0 + 24 24x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 24x + x2 = 24 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 = 24 + 144 Reorder the terms: 144 + 24x + x2 = 24 + 144 Combine like terms: 24 + 144 = 168 144 + 24x + x2 = 168 Factor a perfect square on the left side: (x + 12)(x + 12) = 168 Calculate the square root of the right side: 12.961481397 Break this problem into two subproblems by setting (x + 12) equal to 12.961481397 and -12.961481397.Subproblem 1
x + 12 = 12.961481397 Simplifying x + 12 = 12.961481397 Reorder the terms: 12 + x = 12.961481397 Solving 12 + x = 12.961481397 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 = 12.961481397 + -12 Combine like terms: 12 + -12 = 0 0 + x = 12.961481397 + -12 x = 12.961481397 + -12 Combine like terms: 12.961481397 + -12 = 0.961481397 x = 0.961481397 Simplifying x = 0.961481397Subproblem 2
x + 12 = -12.961481397 Simplifying x + 12 = -12.961481397 Reorder the terms: 12 + x = -12.961481397 Solving 12 + x = -12.961481397 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 = -12.961481397 + -12 Combine like terms: 12 + -12 = 0 0 + x = -12.961481397 + -12 x = -12.961481397 + -12 Combine like terms: -12.961481397 + -12 = -24.961481397 x = -24.961481397 Simplifying x = -24.961481397Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.961481397, -24.961481397}
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