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Simplifying 12x2 + -20x + -3 = 0 Reorder the terms: -3 + -20x + 12x2 = 0 Solving -3 + -20x + 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'. -0.25 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -1.666666667x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -1.666666667x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -1.666666667x + x2 = 0 + 0.25 -1.666666667x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -1.666666667x + x2 = 0.25 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = 0.25 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 0.25 + 0.6944444447 Combine like terms: 0.25 + 0.6944444447 = 0.9444444447 0.6944444447 + -1.666666667x + x2 = 0.9444444447 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 0.9444444447 Calculate the square root of the right side: 0.971825316 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 0.971825316 and -0.971825316.Subproblem 1
x + -0.8333333335 = 0.971825316 Simplifying x + -0.8333333335 = 0.971825316 Reorder the terms: -0.8333333335 + x = 0.971825316 Solving -0.8333333335 + x = 0.971825316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 0.971825316 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 0.971825316 + 0.8333333335 x = 0.971825316 + 0.8333333335 Combine like terms: 0.971825316 + 0.8333333335 = 1.8051586495 x = 1.8051586495 Simplifying x = 1.8051586495Subproblem 2
x + -0.8333333335 = -0.971825316 Simplifying x + -0.8333333335 = -0.971825316 Reorder the terms: -0.8333333335 + x = -0.971825316 Solving -0.8333333335 + x = -0.971825316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -0.971825316 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -0.971825316 + 0.8333333335 x = -0.971825316 + 0.8333333335 Combine like terms: -0.971825316 + 0.8333333335 = -0.1384919825 x = -0.1384919825 Simplifying x = -0.1384919825Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8051586495, -0.1384919825}
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