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Simplifying x2 = 30 + 24x Solving x2 = 30 + 24x Solving for variable 'x'. Reorder the terms: -30 + -24x + x2 = 30 + 24x + -30 + -24x Reorder the terms: -30 + -24x + x2 = 30 + -30 + 24x + -24x Combine like terms: 30 + -30 = 0 -30 + -24x + x2 = 0 + 24x + -24x -30 + -24x + x2 = 24x + -24x Combine like terms: 24x + -24x = 0 -30 + -24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + -24x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -24x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -24x + x2 = 0 + 30 -24x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -24x + x2 = 30 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 = 30 + 144 Reorder the terms: 144 + -24x + x2 = 30 + 144 Combine like terms: 30 + 144 = 174 144 + -24x + x2 = 174 Factor a perfect square on the left side: (x + -12)(x + -12) = 174 Calculate the square root of the right side: 13.190905958 Break this problem into two subproblems by setting (x + -12) equal to 13.190905958 and -13.190905958.Subproblem 1
x + -12 = 13.190905958 Simplifying x + -12 = 13.190905958 Reorder the terms: -12 + x = 13.190905958 Solving -12 + x = 13.190905958 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 = 13.190905958 + 12 Combine like terms: -12 + 12 = 0 0 + x = 13.190905958 + 12 x = 13.190905958 + 12 Combine like terms: 13.190905958 + 12 = 25.190905958 x = 25.190905958 Simplifying x = 25.190905958Subproblem 2
x + -12 = -13.190905958 Simplifying x + -12 = -13.190905958 Reorder the terms: -12 + x = -13.190905958 Solving -12 + x = -13.190905958 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 = -13.190905958 + 12 Combine like terms: -12 + 12 = 0 0 + x = -13.190905958 + 12 x = -13.190905958 + 12 Combine like terms: -13.190905958 + 12 = -1.190905958 x = -1.190905958 Simplifying x = -1.190905958Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.190905958, -1.190905958}
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