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Simplifying 12 + -60x + 5x2 = 0 Solving 12 + -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'. 2.4 + -12x + x2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + -12x + -2.4 + x2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + -12x + x2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + -12x + x2 = 0 + -2.4 -12x + x2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 -12x + x2 = -2.4 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 = -2.4 + 36 Reorder the terms: 36 + -12x + x2 = -2.4 + 36 Combine like terms: -2.4 + 36 = 33.6 36 + -12x + x2 = 33.6 Factor a perfect square on the left side: (x + -6)(x + -6) = 33.6 Calculate the square root of the right side: 5.796550698 Break this problem into two subproblems by setting (x + -6) equal to 5.796550698 and -5.796550698.Subproblem 1
x + -6 = 5.796550698 Simplifying x + -6 = 5.796550698 Reorder the terms: -6 + x = 5.796550698 Solving -6 + x = 5.796550698 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 = 5.796550698 + 6 Combine like terms: -6 + 6 = 0 0 + x = 5.796550698 + 6 x = 5.796550698 + 6 Combine like terms: 5.796550698 + 6 = 11.796550698 x = 11.796550698 Simplifying x = 11.796550698Subproblem 2
x + -6 = -5.796550698 Simplifying x + -6 = -5.796550698 Reorder the terms: -6 + x = -5.796550698 Solving -6 + x = -5.796550698 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 = -5.796550698 + 6 Combine like terms: -6 + 6 = 0 0 + x = -5.796550698 + 6 x = -5.796550698 + 6 Combine like terms: -5.796550698 + 6 = 0.203449302 x = 0.203449302 Simplifying x = 0.203449302Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.796550698, 0.203449302}
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