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Simplifying x2 + -12x + -20.25 = 0 Reorder the terms: -20.25 + -12x + x2 = 0 Solving -20.25 + -12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '20.25' to each side of the equation. -20.25 + -12x + 20.25 + x2 = 0 + 20.25 Reorder the terms: -20.25 + 20.25 + -12x + x2 = 0 + 20.25 Combine like terms: -20.25 + 20.25 = 0.00 0.00 + -12x + x2 = 0 + 20.25 -12x + x2 = 0 + 20.25 Combine like terms: 0 + 20.25 = 20.25 -12x + x2 = 20.25 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 = 20.25 + 36 Reorder the terms: 36 + -12x + x2 = 20.25 + 36 Combine like terms: 20.25 + 36 = 56.25 36 + -12x + x2 = 56.25 Factor a perfect square on the left side: (x + -6)(x + -6) = 56.25 Calculate the square root of the right side: 7.5 Break this problem into two subproblems by setting (x + -6) equal to 7.5 and -7.5.Subproblem 1
x + -6 = 7.5 Simplifying x + -6 = 7.5 Reorder the terms: -6 + x = 7.5 Solving -6 + x = 7.5 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 = 7.5 + 6 Combine like terms: -6 + 6 = 0 0 + x = 7.5 + 6 x = 7.5 + 6 Combine like terms: 7.5 + 6 = 13.5 x = 13.5 Simplifying x = 13.5Subproblem 2
x + -6 = -7.5 Simplifying x + -6 = -7.5 Reorder the terms: -6 + x = -7.5 Solving -6 + x = -7.5 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 = -7.5 + 6 Combine like terms: -6 + 6 = 0 0 + x = -7.5 + 6 x = -7.5 + 6 Combine like terms: -7.5 + 6 = -1.5 x = -1.5 Simplifying x = -1.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.5, -1.5}
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