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Simplifying 24 = -1x2 + 24x Reorder the terms: 24 = 24x + -1x2 Solving 24 = 24x + -1x2 Solving for variable 'x'. Reorder the terms: 24 + -24x + x2 = 24x + -24x + -1x2 + x2 Combine like terms: 24x + -24x = 0 24 + -24x + x2 = 0 + -1x2 + x2 24 + -24x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 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 = 120 144 + -24x + x2 = 120 Factor a perfect square on the left side: (x + -12)(x + -12) = 120 Calculate the square root of the right side: 10.95445115 Break this problem into two subproblems by setting (x + -12) equal to 10.95445115 and -10.95445115.Subproblem 1
x + -12 = 10.95445115 Simplifying x + -12 = 10.95445115 Reorder the terms: -12 + x = 10.95445115 Solving -12 + x = 10.95445115 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 = 10.95445115 + 12 Combine like terms: -12 + 12 = 0 0 + x = 10.95445115 + 12 x = 10.95445115 + 12 Combine like terms: 10.95445115 + 12 = 22.95445115 x = 22.95445115 Simplifying x = 22.95445115Subproblem 2
x + -12 = -10.95445115 Simplifying x + -12 = -10.95445115 Reorder the terms: -12 + x = -10.95445115 Solving -12 + x = -10.95445115 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 = -10.95445115 + 12 Combine like terms: -12 + 12 = 0 0 + x = -10.95445115 + 12 x = -10.95445115 + 12 Combine like terms: -10.95445115 + 12 = 1.04554885 x = 1.04554885 Simplifying x = 1.04554885Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.95445115, 1.04554885}
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