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Simplifying 5x2 + -60x + 108 = 0 Reorder the terms: 108 + -60x + 5x2 = 0 Solving 108 + -60x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 21.6 + -12x + x2 = 0 Move the constant term to the right: Add '-21.6' to each side of the equation. 21.6 + -12x + -21.6 + x2 = 0 + -21.6 Reorder the terms: 21.6 + -21.6 + -12x + x2 = 0 + -21.6 Combine like terms: 21.6 + -21.6 = 0.0 0.0 + -12x + x2 = 0 + -21.6 -12x + x2 = 0 + -21.6 Combine like terms: 0 + -21.6 = -21.6 -12x + x2 = -21.6 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 = -21.6 + 36 Reorder the terms: 36 + -12x + x2 = -21.6 + 36 Combine like terms: -21.6 + 36 = 14.4 36 + -12x + x2 = 14.4 Factor a perfect square on the left side: (x + -6)(x + -6) = 14.4 Calculate the square root of the right side: 3.794733192 Break this problem into two subproblems by setting (x + -6) equal to 3.794733192 and -3.794733192.Subproblem 1
x + -6 = 3.794733192 Simplifying x + -6 = 3.794733192 Reorder the terms: -6 + x = 3.794733192 Solving -6 + x = 3.794733192 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 = 3.794733192 + 6 Combine like terms: -6 + 6 = 0 0 + x = 3.794733192 + 6 x = 3.794733192 + 6 Combine like terms: 3.794733192 + 6 = 9.794733192 x = 9.794733192 Simplifying x = 9.794733192Subproblem 2
x + -6 = -3.794733192 Simplifying x + -6 = -3.794733192 Reorder the terms: -6 + x = -3.794733192 Solving -6 + x = -3.794733192 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 = -3.794733192 + 6 Combine like terms: -6 + 6 = 0 0 + x = -3.794733192 + 6 x = -3.794733192 + 6 Combine like terms: -3.794733192 + 6 = 2.205266808 x = 2.205266808 Simplifying x = 2.205266808Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.794733192, 2.205266808}
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