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Simplifying x2 + -24x = 33 Reorder the terms: -24x + x2 = 33 Solving -24x + x2 = 33 Solving for variable 'x'. Reorder the terms: -33 + -24x + x2 = 33 + -33 Combine like terms: 33 + -33 = 0 -33 + -24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '33' to each side of the equation. -33 + -24x + 33 + x2 = 0 + 33 Reorder the terms: -33 + 33 + -24x + x2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + -24x + x2 = 0 + 33 -24x + x2 = 0 + 33 Combine like terms: 0 + 33 = 33 -24x + x2 = 33 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 = 33 + 144 Reorder the terms: 144 + -24x + x2 = 33 + 144 Combine like terms: 33 + 144 = 177 144 + -24x + x2 = 177 Factor a perfect square on the left side: (x + -12)(x + -12) = 177 Calculate the square root of the right side: 13.304134696 Break this problem into two subproblems by setting (x + -12) equal to 13.304134696 and -13.304134696.Subproblem 1
x + -12 = 13.304134696 Simplifying x + -12 = 13.304134696 Reorder the terms: -12 + x = 13.304134696 Solving -12 + x = 13.304134696 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 = 13.304134696 + 12 Combine like terms: -12 + 12 = 0 0 + x = 13.304134696 + 12 x = 13.304134696 + 12 Combine like terms: 13.304134696 + 12 = 25.304134696 x = 25.304134696 Simplifying x = 25.304134696Subproblem 2
x + -12 = -13.304134696 Simplifying x + -12 = -13.304134696 Reorder the terms: -12 + x = -13.304134696 Solving -12 + x = -13.304134696 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 = -13.304134696 + 12 Combine like terms: -12 + 12 = 0 0 + x = -13.304134696 + 12 x = -13.304134696 + 12 Combine like terms: -13.304134696 + 12 = -1.304134696 x = -1.304134696 Simplifying x = -1.304134696Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.304134696, -1.304134696}
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