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Simplifying 0 = x2 + -24x + -36 Reorder the terms: 0 = -36 + -24x + x2 Solving 0 = -36 + -24x + x2 Solving for variable 'x'. Combine like terms: 0 + 36 = 36 36 + 24x + -1x2 = -36 + -24x + x2 + 36 + 24x + -1x2 Reorder the terms: 36 + 24x + -1x2 = -36 + 36 + -24x + 24x + x2 + -1x2 Combine like terms: -36 + 36 = 0 36 + 24x + -1x2 = 0 + -24x + 24x + x2 + -1x2 36 + 24x + -1x2 = -24x + 24x + x2 + -1x2 Combine like terms: -24x + 24x = 0 36 + 24x + -1x2 = 0 + x2 + -1x2 36 + 24x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 36 + 24x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -36 + -24x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + -24x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -24x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -24x + x2 = 0 + 36 -24x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -24x + x2 = 36 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 = 36 + 144 Reorder the terms: 144 + -24x + x2 = 36 + 144 Combine like terms: 36 + 144 = 180 144 + -24x + x2 = 180 Factor a perfect square on the left side: (x + -12)(x + -12) = 180 Calculate the square root of the right side: 13.416407865 Break this problem into two subproblems by setting (x + -12) equal to 13.416407865 and -13.416407865.Subproblem 1
x + -12 = 13.416407865 Simplifying x + -12 = 13.416407865 Reorder the terms: -12 + x = 13.416407865 Solving -12 + x = 13.416407865 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 = 13.416407865 + 12 Combine like terms: -12 + 12 = 0 0 + x = 13.416407865 + 12 x = 13.416407865 + 12 Combine like terms: 13.416407865 + 12 = 25.416407865 x = 25.416407865 Simplifying x = 25.416407865Subproblem 2
x + -12 = -13.416407865 Simplifying x + -12 = -13.416407865 Reorder the terms: -12 + x = -13.416407865 Solving -12 + x = -13.416407865 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 = -13.416407865 + 12 Combine like terms: -12 + 12 = 0 0 + x = -13.416407865 + 12 x = -13.416407865 + 12 Combine like terms: -13.416407865 + 12 = -1.416407865 x = -1.416407865 Simplifying x = -1.416407865Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.416407865, -1.416407865}
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