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Simplifying x2 + -24x + 93 = 0 Reorder the terms: 93 + -24x + x2 = 0 Solving 93 + -24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-93' to each side of the equation. 93 + -24x + -93 + x2 = 0 + -93 Reorder the terms: 93 + -93 + -24x + x2 = 0 + -93 Combine like terms: 93 + -93 = 0 0 + -24x + x2 = 0 + -93 -24x + x2 = 0 + -93 Combine like terms: 0 + -93 = -93 -24x + x2 = -93 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 = -93 + 144 Reorder the terms: 144 + -24x + x2 = -93 + 144 Combine like terms: -93 + 144 = 51 144 + -24x + x2 = 51 Factor a perfect square on the left side: (x + -12)(x + -12) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (x + -12) equal to 7.141428429 and -7.141428429.Subproblem 1
x + -12 = 7.141428429 Simplifying x + -12 = 7.141428429 Reorder the terms: -12 + x = 7.141428429 Solving -12 + x = 7.141428429 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 = 7.141428429 + 12 Combine like terms: -12 + 12 = 0 0 + x = 7.141428429 + 12 x = 7.141428429 + 12 Combine like terms: 7.141428429 + 12 = 19.141428429 x = 19.141428429 Simplifying x = 19.141428429Subproblem 2
x + -12 = -7.141428429 Simplifying x + -12 = -7.141428429 Reorder the terms: -12 + x = -7.141428429 Solving -12 + x = -7.141428429 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 = -7.141428429 + 12 Combine like terms: -12 + 12 = 0 0 + x = -7.141428429 + 12 x = -7.141428429 + 12 Combine like terms: -7.141428429 + 12 = 4.858571571 x = 4.858571571 Simplifying x = 4.858571571Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.141428429, 4.858571571}
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