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Simplifying 12 = 20x + -5x2 Solving 12 = 20x + -5x2 Solving for variable 'x'. Reorder the terms: 12 + -20x + 5x2 = 20x + -20x + -5x2 + 5x2 Combine like terms: 20x + -20x = 0 12 + -20x + 5x2 = 0 + -5x2 + 5x2 12 + -20x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 12 + -20x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.4 + -4x + x2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + -4x + -2.4 + x2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + -4x + x2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + -4x + x2 = 0 + -2.4 -4x + x2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 -4x + x2 = -2.4 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -2.4 + 4 Reorder the terms: 4 + -4x + x2 = -2.4 + 4 Combine like terms: -2.4 + 4 = 1.6 4 + -4x + x2 = 1.6 Factor a perfect square on the left side: (x + -2)(x + -2) = 1.6 Calculate the square root of the right side: 1.264911064 Break this problem into two subproblems by setting (x + -2) equal to 1.264911064 and -1.264911064.Subproblem 1
x + -2 = 1.264911064 Simplifying x + -2 = 1.264911064 Reorder the terms: -2 + x = 1.264911064 Solving -2 + x = 1.264911064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.264911064 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.264911064 + 2 x = 1.264911064 + 2 Combine like terms: 1.264911064 + 2 = 3.264911064 x = 3.264911064 Simplifying x = 3.264911064Subproblem 2
x + -2 = -1.264911064 Simplifying x + -2 = -1.264911064 Reorder the terms: -2 + x = -1.264911064 Solving -2 + x = -1.264911064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.264911064 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.264911064 + 2 x = -1.264911064 + 2 Combine like terms: -1.264911064 + 2 = 0.735088936 x = 0.735088936 Simplifying x = 0.735088936Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.264911064, 0.735088936}
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