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Simplifying 0 = 1.7 + 12x + -5x2 Solving 0 = 1.7 + 12x + -5x2 Solving for variable 'x'. Combine like terms: 0 + -1.7 = -1.7 -1.7 + -12x + 5x2 = 1.7 + 12x + -5x2 + -1.7 + -12x + 5x2 Reorder the terms: -1.7 + -12x + 5x2 = 1.7 + -1.7 + 12x + -12x + -5x2 + 5x2 Combine like terms: 1.7 + -1.7 = 0.0 -1.7 + -12x + 5x2 = 0.0 + 12x + -12x + -5x2 + 5x2 -1.7 + -12x + 5x2 = 12x + -12x + -5x2 + 5x2 Combine like terms: 12x + -12x = 0 -1.7 + -12x + 5x2 = 0 + -5x2 + 5x2 -1.7 + -12x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -1.7 + -12x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.34 + -2.4x + x2 = 0 Move the constant term to the right: Add '0.34' to each side of the equation. -0.34 + -2.4x + 0.34 + x2 = 0 + 0.34 Reorder the terms: -0.34 + 0.34 + -2.4x + x2 = 0 + 0.34 Combine like terms: -0.34 + 0.34 = 0.00 0.00 + -2.4x + x2 = 0 + 0.34 -2.4x + x2 = 0 + 0.34 Combine like terms: 0 + 0.34 = 0.34 -2.4x + x2 = 0.34 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = 0.34 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = 0.34 + 1.44 Combine like terms: 0.34 + 1.44 = 1.78 1.44 + -2.4x + x2 = 1.78 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 1.78 Calculate the square root of the right side: 1.334166406 Break this problem into two subproblems by setting (x + -1.2) equal to 1.334166406 and -1.334166406.Subproblem 1
x + -1.2 = 1.334166406 Simplifying x + -1.2 = 1.334166406 Reorder the terms: -1.2 + x = 1.334166406 Solving -1.2 + x = 1.334166406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 1.334166406 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 1.334166406 + 1.2 x = 1.334166406 + 1.2 Combine like terms: 1.334166406 + 1.2 = 2.534166406 x = 2.534166406 Simplifying x = 2.534166406Subproblem 2
x + -1.2 = -1.334166406 Simplifying x + -1.2 = -1.334166406 Reorder the terms: -1.2 + x = -1.334166406 Solving -1.2 + x = -1.334166406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -1.334166406 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -1.334166406 + 1.2 x = -1.334166406 + 1.2 Combine like terms: -1.334166406 + 1.2 = -0.134166406 x = -0.134166406 Simplifying x = -0.134166406Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.534166406, -0.134166406}
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