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Simplifying 12 = -1x2 + 24x Reorder the terms: 12 = 24x + -1x2 Solving 12 = 24x + -1x2 Solving for variable 'x'. Reorder the terms: 12 + -24x + x2 = 24x + -24x + -1x2 + x2 Combine like terms: 24x + -24x = 0 12 + -24x + x2 = 0 + -1x2 + x2 12 + -24x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 12 + -24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -24x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -24x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -24x + x2 = 0 + -12 -24x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -24x + x2 = -12 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 = -12 + 144 Reorder the terms: 144 + -24x + x2 = -12 + 144 Combine like terms: -12 + 144 = 132 144 + -24x + x2 = 132 Factor a perfect square on the left side: (x + -12)(x + -12) = 132 Calculate the square root of the right side: 11.489125293 Break this problem into two subproblems by setting (x + -12) equal to 11.489125293 and -11.489125293.Subproblem 1
x + -12 = 11.489125293 Simplifying x + -12 = 11.489125293 Reorder the terms: -12 + x = 11.489125293 Solving -12 + x = 11.489125293 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 = 11.489125293 + 12 Combine like terms: -12 + 12 = 0 0 + x = 11.489125293 + 12 x = 11.489125293 + 12 Combine like terms: 11.489125293 + 12 = 23.489125293 x = 23.489125293 Simplifying x = 23.489125293Subproblem 2
x + -12 = -11.489125293 Simplifying x + -12 = -11.489125293 Reorder the terms: -12 + x = -11.489125293 Solving -12 + x = -11.489125293 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 = -11.489125293 + 12 Combine like terms: -12 + 12 = 0 0 + x = -11.489125293 + 12 x = -11.489125293 + 12 Combine like terms: -11.489125293 + 12 = 0.510874707 x = 0.510874707 Simplifying x = 0.510874707Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.489125293, 0.510874707}
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