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Simplifying x2 + -12x + -22.5 = 0 Reorder the terms: -22.5 + -12x + x2 = 0 Solving -22.5 + -12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '22.5' to each side of the equation. -22.5 + -12x + 22.5 + x2 = 0 + 22.5 Reorder the terms: -22.5 + 22.5 + -12x + x2 = 0 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + -12x + x2 = 0 + 22.5 -12x + x2 = 0 + 22.5 Combine like terms: 0 + 22.5 = 22.5 -12x + x2 = 22.5 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 22.5 + 36 Reorder the terms: 36 + -12x + x2 = 22.5 + 36 Combine like terms: 22.5 + 36 = 58.5 36 + -12x + x2 = 58.5 Factor a perfect square on the left side: (x + -6)(x + -6) = 58.5 Calculate the square root of the right side: 7.64852927 Break this problem into two subproblems by setting (x + -6) equal to 7.64852927 and -7.64852927.Subproblem 1
x + -6 = 7.64852927 Simplifying x + -6 = 7.64852927 Reorder the terms: -6 + x = 7.64852927 Solving -6 + x = 7.64852927 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 7.64852927 + 6 Combine like terms: -6 + 6 = 0 0 + x = 7.64852927 + 6 x = 7.64852927 + 6 Combine like terms: 7.64852927 + 6 = 13.64852927 x = 13.64852927 Simplifying x = 13.64852927Subproblem 2
x + -6 = -7.64852927 Simplifying x + -6 = -7.64852927 Reorder the terms: -6 + x = -7.64852927 Solving -6 + x = -7.64852927 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -7.64852927 + 6 Combine like terms: -6 + 6 = 0 0 + x = -7.64852927 + 6 x = -7.64852927 + 6 Combine like terms: -7.64852927 + 6 = -1.64852927 x = -1.64852927 Simplifying x = -1.64852927Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.64852927, -1.64852927}
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