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Simplifying 12x2 + -19x = 22 Reorder the terms: -19x + 12x2 = 22 Solving -19x + 12x2 = 22 Solving for variable 'x'. Reorder the terms: -22 + -19x + 12x2 = 22 + -22 Combine like terms: 22 + -22 = 0 -22 + -19x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1.833333333 + -1.583333333x + x2 = 0 Move the constant term to the right: Add '1.833333333' to each side of the equation. -1.833333333 + -1.583333333x + 1.833333333 + x2 = 0 + 1.833333333 Reorder the terms: -1.833333333 + 1.833333333 + -1.583333333x + x2 = 0 + 1.833333333 Combine like terms: -1.833333333 + 1.833333333 = 0.000000000 0.000000000 + -1.583333333x + x2 = 0 + 1.833333333 -1.583333333x + x2 = 0 + 1.833333333 Combine like terms: 0 + 1.833333333 = 1.833333333 -1.583333333x + x2 = 1.833333333 The x term is -1.583333333x. Take half its coefficient (-0.7916666665). Square it (0.6267361108) and add it to both sides. Add '0.6267361108' to each side of the equation. -1.583333333x + 0.6267361108 + x2 = 1.833333333 + 0.6267361108 Reorder the terms: 0.6267361108 + -1.583333333x + x2 = 1.833333333 + 0.6267361108 Combine like terms: 1.833333333 + 0.6267361108 = 2.4600694438 0.6267361108 + -1.583333333x + x2 = 2.4600694438 Factor a perfect square on the left side: (x + -0.7916666665)(x + -0.7916666665) = 2.4600694438 Calculate the square root of the right side: 1.568460852 Break this problem into two subproblems by setting (x + -0.7916666665) equal to 1.568460852 and -1.568460852.Subproblem 1
x + -0.7916666665 = 1.568460852 Simplifying x + -0.7916666665 = 1.568460852 Reorder the terms: -0.7916666665 + x = 1.568460852 Solving -0.7916666665 + x = 1.568460852 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7916666665' to each side of the equation. -0.7916666665 + 0.7916666665 + x = 1.568460852 + 0.7916666665 Combine like terms: -0.7916666665 + 0.7916666665 = 0.0000000000 0.0000000000 + x = 1.568460852 + 0.7916666665 x = 1.568460852 + 0.7916666665 Combine like terms: 1.568460852 + 0.7916666665 = 2.3601275185 x = 2.3601275185 Simplifying x = 2.3601275185Subproblem 2
x + -0.7916666665 = -1.568460852 Simplifying x + -0.7916666665 = -1.568460852 Reorder the terms: -0.7916666665 + x = -1.568460852 Solving -0.7916666665 + x = -1.568460852 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7916666665' to each side of the equation. -0.7916666665 + 0.7916666665 + x = -1.568460852 + 0.7916666665 Combine like terms: -0.7916666665 + 0.7916666665 = 0.0000000000 0.0000000000 + x = -1.568460852 + 0.7916666665 x = -1.568460852 + 0.7916666665 Combine like terms: -1.568460852 + 0.7916666665 = -0.7767941855 x = -0.7767941855 Simplifying x = -0.7767941855Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3601275185, -0.7767941855}
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