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Simplifying x2 + -24x + -28 = 0 Reorder the terms: -28 + -24x + x2 = 0 Solving -28 + -24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + -24x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + -24x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -24x + x2 = 0 + 28 -24x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 -24x + x2 = 28 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 = 28 + 144 Reorder the terms: 144 + -24x + x2 = 28 + 144 Combine like terms: 28 + 144 = 172 144 + -24x + x2 = 172 Factor a perfect square on the left side: (x + -12)(x + -12) = 172 Calculate the square root of the right side: 13.114877049 Break this problem into two subproblems by setting (x + -12) equal to 13.114877049 and -13.114877049.Subproblem 1
x + -12 = 13.114877049 Simplifying x + -12 = 13.114877049 Reorder the terms: -12 + x = 13.114877049 Solving -12 + x = 13.114877049 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 = 13.114877049 + 12 Combine like terms: -12 + 12 = 0 0 + x = 13.114877049 + 12 x = 13.114877049 + 12 Combine like terms: 13.114877049 + 12 = 25.114877049 x = 25.114877049 Simplifying x = 25.114877049Subproblem 2
x + -12 = -13.114877049 Simplifying x + -12 = -13.114877049 Reorder the terms: -12 + x = -13.114877049 Solving -12 + x = -13.114877049 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 = -13.114877049 + 12 Combine like terms: -12 + 12 = 0 0 + x = -13.114877049 + 12 x = -13.114877049 + 12 Combine like terms: -13.114877049 + 12 = -1.114877049 x = -1.114877049 Simplifying x = -1.114877049Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.114877049, -1.114877049}
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