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Simplifying x2 + -24x + 81 = 0 Reorder the terms: 81 + -24x + x2 = 0 Solving 81 + -24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-81' to each side of the equation. 81 + -24x + -81 + x2 = 0 + -81 Reorder the terms: 81 + -81 + -24x + x2 = 0 + -81 Combine like terms: 81 + -81 = 0 0 + -24x + x2 = 0 + -81 -24x + x2 = 0 + -81 Combine like terms: 0 + -81 = -81 -24x + x2 = -81 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 = -81 + 144 Reorder the terms: 144 + -24x + x2 = -81 + 144 Combine like terms: -81 + 144 = 63 144 + -24x + x2 = 63 Factor a perfect square on the left side: (x + -12)(x + -12) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (x + -12) equal to 7.937253933 and -7.937253933.Subproblem 1
x + -12 = 7.937253933 Simplifying x + -12 = 7.937253933 Reorder the terms: -12 + x = 7.937253933 Solving -12 + x = 7.937253933 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 = 7.937253933 + 12 Combine like terms: -12 + 12 = 0 0 + x = 7.937253933 + 12 x = 7.937253933 + 12 Combine like terms: 7.937253933 + 12 = 19.937253933 x = 19.937253933 Simplifying x = 19.937253933Subproblem 2
x + -12 = -7.937253933 Simplifying x + -12 = -7.937253933 Reorder the terms: -12 + x = -7.937253933 Solving -12 + x = -7.937253933 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 = -7.937253933 + 12 Combine like terms: -12 + 12 = 0 0 + x = -7.937253933 + 12 x = -7.937253933 + 12 Combine like terms: -7.937253933 + 12 = 4.062746067 x = 4.062746067 Simplifying x = 4.062746067Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.937253933, 4.062746067}
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