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Simplifying 3.92x + -0.48x2 = 0.5 Solving 3.92x + -0.48x2 = 0.5 Solving for variable 'x'. Reorder the terms: -0.5 + 3.92x + -0.48x2 = 0.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 -0.5 + 3.92x + -0.48x2 = 0.0 Begin completing the square. Divide all terms by -0.48 the coefficient of the squared term: Divide each side by '-0.48'. 1.041666667 + -8.166666667x + x2 = 0 Move the constant term to the right: Add '-1.041666667' to each side of the equation. 1.041666667 + -8.166666667x + -1.041666667 + x2 = 0 + -1.041666667 Reorder the terms: 1.041666667 + -1.041666667 + -8.166666667x + x2 = 0 + -1.041666667 Combine like terms: 1.041666667 + -1.041666667 = 0.000000000 0.000000000 + -8.166666667x + x2 = 0 + -1.041666667 -8.166666667x + x2 = 0 + -1.041666667 Combine like terms: 0 + -1.041666667 = -1.041666667 -8.166666667x + x2 = -1.041666667 The x term is -8.166666667x. Take half its coefficient (-4.083333334). Square it (16.67361112) and add it to both sides. Add '16.67361112' to each side of the equation. -8.166666667x + 16.67361112 + x2 = -1.041666667 + 16.67361112 Reorder the terms: 16.67361112 + -8.166666667x + x2 = -1.041666667 + 16.67361112 Combine like terms: -1.041666667 + 16.67361112 = 15.631944453 16.67361112 + -8.166666667x + x2 = 15.631944453 Factor a perfect square on the left side: (x + -4.083333334)(x + -4.083333334) = 15.631944453 Calculate the square root of the right side: 3.953725389 Break this problem into two subproblems by setting (x + -4.083333334) equal to 3.953725389 and -3.953725389.Subproblem 1
x + -4.083333334 = 3.953725389 Simplifying x + -4.083333334 = 3.953725389 Reorder the terms: -4.083333334 + x = 3.953725389 Solving -4.083333334 + x = 3.953725389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.083333334' to each side of the equation. -4.083333334 + 4.083333334 + x = 3.953725389 + 4.083333334 Combine like terms: -4.083333334 + 4.083333334 = 0.000000000 0.000000000 + x = 3.953725389 + 4.083333334 x = 3.953725389 + 4.083333334 Combine like terms: 3.953725389 + 4.083333334 = 8.037058723 x = 8.037058723 Simplifying x = 8.037058723Subproblem 2
x + -4.083333334 = -3.953725389 Simplifying x + -4.083333334 = -3.953725389 Reorder the terms: -4.083333334 + x = -3.953725389 Solving -4.083333334 + x = -3.953725389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.083333334' to each side of the equation. -4.083333334 + 4.083333334 + x = -3.953725389 + 4.083333334 Combine like terms: -4.083333334 + 4.083333334 = 0.000000000 0.000000000 + x = -3.953725389 + 4.083333334 x = -3.953725389 + 4.083333334 Combine like terms: -3.953725389 + 4.083333334 = 0.129607945 x = 0.129607945 Simplifying x = 0.129607945Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.037058723, 0.129607945}
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