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Simplifying 12x2 + 60x + 71 = 0 Reorder the terms: 71 + 60x + 12x2 = 0 Solving 71 + 60x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 5.916666667 + 5x + x2 = 0 Move the constant term to the right: Add '-5.916666667' to each side of the equation. 5.916666667 + 5x + -5.916666667 + x2 = 0 + -5.916666667 Reorder the terms: 5.916666667 + -5.916666667 + 5x + x2 = 0 + -5.916666667 Combine like terms: 5.916666667 + -5.916666667 = 0.000000000 0.000000000 + 5x + x2 = 0 + -5.916666667 5x + x2 = 0 + -5.916666667 Combine like terms: 0 + -5.916666667 = -5.916666667 5x + x2 = -5.916666667 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -5.916666667 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -5.916666667 + 6.25 Combine like terms: -5.916666667 + 6.25 = 0.333333333 6.25 + 5x + x2 = 0.333333333 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 0.333333333 Calculate the square root of the right side: 0.577350269 Break this problem into two subproblems by setting (x + 2.5) equal to 0.577350269 and -0.577350269.Subproblem 1
x + 2.5 = 0.577350269 Simplifying x + 2.5 = 0.577350269 Reorder the terms: 2.5 + x = 0.577350269 Solving 2.5 + x = 0.577350269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 0.577350269 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 0.577350269 + -2.5 x = 0.577350269 + -2.5 Combine like terms: 0.577350269 + -2.5 = -1.922649731 x = -1.922649731 Simplifying x = -1.922649731Subproblem 2
x + 2.5 = -0.577350269 Simplifying x + 2.5 = -0.577350269 Reorder the terms: 2.5 + x = -0.577350269 Solving 2.5 + x = -0.577350269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -0.577350269 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -0.577350269 + -2.5 x = -0.577350269 + -2.5 Combine like terms: -0.577350269 + -2.5 = -3.077350269 x = -3.077350269 Simplifying x = -3.077350269Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.922649731, -3.077350269}
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