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Simplifying x2 + -24x + 86 = 0 Reorder the terms: 86 + -24x + x2 = 0 Solving 86 + -24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-86' to each side of the equation. 86 + -24x + -86 + x2 = 0 + -86 Reorder the terms: 86 + -86 + -24x + x2 = 0 + -86 Combine like terms: 86 + -86 = 0 0 + -24x + x2 = 0 + -86 -24x + x2 = 0 + -86 Combine like terms: 0 + -86 = -86 -24x + x2 = -86 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 = -86 + 144 Reorder the terms: 144 + -24x + x2 = -86 + 144 Combine like terms: -86 + 144 = 58 144 + -24x + x2 = 58 Factor a perfect square on the left side: (x + -12)(x + -12) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (x + -12) equal to 7.615773106 and -7.615773106.Subproblem 1
x + -12 = 7.615773106 Simplifying x + -12 = 7.615773106 Reorder the terms: -12 + x = 7.615773106 Solving -12 + x = 7.615773106 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 = 7.615773106 + 12 Combine like terms: -12 + 12 = 0 0 + x = 7.615773106 + 12 x = 7.615773106 + 12 Combine like terms: 7.615773106 + 12 = 19.615773106 x = 19.615773106 Simplifying x = 19.615773106Subproblem 2
x + -12 = -7.615773106 Simplifying x + -12 = -7.615773106 Reorder the terms: -12 + x = -7.615773106 Solving -12 + x = -7.615773106 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 = -7.615773106 + 12 Combine like terms: -12 + 12 = 0 0 + x = -7.615773106 + 12 x = -7.615773106 + 12 Combine like terms: -7.615773106 + 12 = 4.384226894 x = 4.384226894 Simplifying x = 4.384226894Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.615773106, 4.384226894}
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