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Simplifying 5x2 + -60x + 36 = 0 Reorder the terms: 36 + -60x + 5x2 = 0 Solving 36 + -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'. 7.2 + -12x + x2 = 0 Move the constant term to the right: Add '-7.2' to each side of the equation. 7.2 + -12x + -7.2 + x2 = 0 + -7.2 Reorder the terms: 7.2 + -7.2 + -12x + x2 = 0 + -7.2 Combine like terms: 7.2 + -7.2 = 0.0 0.0 + -12x + x2 = 0 + -7.2 -12x + x2 = 0 + -7.2 Combine like terms: 0 + -7.2 = -7.2 -12x + x2 = -7.2 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 = -7.2 + 36 Reorder the terms: 36 + -12x + x2 = -7.2 + 36 Combine like terms: -7.2 + 36 = 28.8 36 + -12x + x2 = 28.8 Factor a perfect square on the left side: (x + -6)(x + -6) = 28.8 Calculate the square root of the right side: 5.366563146 Break this problem into two subproblems by setting (x + -6) equal to 5.366563146 and -5.366563146.Subproblem 1
x + -6 = 5.366563146 Simplifying x + -6 = 5.366563146 Reorder the terms: -6 + x = 5.366563146 Solving -6 + x = 5.366563146 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 = 5.366563146 + 6 Combine like terms: -6 + 6 = 0 0 + x = 5.366563146 + 6 x = 5.366563146 + 6 Combine like terms: 5.366563146 + 6 = 11.366563146 x = 11.366563146 Simplifying x = 11.366563146Subproblem 2
x + -6 = -5.366563146 Simplifying x + -6 = -5.366563146 Reorder the terms: -6 + x = -5.366563146 Solving -6 + x = -5.366563146 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 = -5.366563146 + 6 Combine like terms: -6 + 6 = 0 0 + x = -5.366563146 + 6 x = -5.366563146 + 6 Combine like terms: -5.366563146 + 6 = 0.633436854 x = 0.633436854 Simplifying x = 0.633436854Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.366563146, 0.633436854}
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