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Simplifying x2 + 24x = 63 Reorder the terms: 24x + x2 = 63 Solving 24x + x2 = 63 Solving for variable 'x'. Reorder the terms: -63 + 24x + x2 = 63 + -63 Combine like terms: 63 + -63 = 0 -63 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '63' to each side of the equation. -63 + 24x + 63 + x2 = 0 + 63 Reorder the terms: -63 + 63 + 24x + x2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + 24x + x2 = 0 + 63 24x + x2 = 0 + 63 Combine like terms: 0 + 63 = 63 24x + x2 = 63 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 = 63 + 144 Reorder the terms: 144 + 24x + x2 = 63 + 144 Combine like terms: 63 + 144 = 207 144 + 24x + x2 = 207 Factor a perfect square on the left side: (x + 12)(x + 12) = 207 Calculate the square root of the right side: 14.38749457 Break this problem into two subproblems by setting (x + 12) equal to 14.38749457 and -14.38749457.Subproblem 1
x + 12 = 14.38749457 Simplifying x + 12 = 14.38749457 Reorder the terms: 12 + x = 14.38749457 Solving 12 + x = 14.38749457 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 = 14.38749457 + -12 Combine like terms: 12 + -12 = 0 0 + x = 14.38749457 + -12 x = 14.38749457 + -12 Combine like terms: 14.38749457 + -12 = 2.38749457 x = 2.38749457 Simplifying x = 2.38749457Subproblem 2
x + 12 = -14.38749457 Simplifying x + 12 = -14.38749457 Reorder the terms: 12 + x = -14.38749457 Solving 12 + x = -14.38749457 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 = -14.38749457 + -12 Combine like terms: 12 + -12 = 0 0 + x = -14.38749457 + -12 x = -14.38749457 + -12 Combine like terms: -14.38749457 + -12 = -26.38749457 x = -26.38749457 Simplifying x = -26.38749457Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.38749457, -26.38749457}
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