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Simplifying 0.06x2 + 0.31x + 4 = 10 Reorder the terms: 4 + 0.31x + 0.06x2 = 10 Solving 4 + 0.31x + 0.06x2 = 10 Solving for variable 'x'. Reorder the terms: 4 + -10 + 0.31x + 0.06x2 = 10 + -10 Combine like terms: 4 + -10 = -6 -6 + 0.31x + 0.06x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -6 + 0.31x + 0.06x2 = 0 Begin completing the square. Divide all terms by 0.06 the coefficient of the squared term: Divide each side by '0.06'. -100 + 5.166666667x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + 5.166666667x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 5.166666667x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 5.166666667x + x2 = 0 + 100 5.166666667x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 5.166666667x + x2 = 100 The x term is 5.166666667x. Take half its coefficient (2.583333334). Square it (6.673611115) and add it to both sides. Add '6.673611115' to each side of the equation. 5.166666667x + 6.673611115 + x2 = 100 + 6.673611115 Reorder the terms: 6.673611115 + 5.166666667x + x2 = 100 + 6.673611115 Combine like terms: 100 + 6.673611115 = 106.673611115 6.673611115 + 5.166666667x + x2 = 106.673611115 Factor a perfect square on the left side: (x + 2.583333334)(x + 2.583333334) = 106.673611115 Calculate the square root of the right side: 10.328291781 Break this problem into two subproblems by setting (x + 2.583333334) equal to 10.328291781 and -10.328291781.Subproblem 1
x + 2.583333334 = 10.328291781 Simplifying x + 2.583333334 = 10.328291781 Reorder the terms: 2.583333334 + x = 10.328291781 Solving 2.583333334 + x = 10.328291781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.583333334' to each side of the equation. 2.583333334 + -2.583333334 + x = 10.328291781 + -2.583333334 Combine like terms: 2.583333334 + -2.583333334 = 0.000000000 0.000000000 + x = 10.328291781 + -2.583333334 x = 10.328291781 + -2.583333334 Combine like terms: 10.328291781 + -2.583333334 = 7.744958447 x = 7.744958447 Simplifying x = 7.744958447Subproblem 2
x + 2.583333334 = -10.328291781 Simplifying x + 2.583333334 = -10.328291781 Reorder the terms: 2.583333334 + x = -10.328291781 Solving 2.583333334 + x = -10.328291781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.583333334' to each side of the equation. 2.583333334 + -2.583333334 + x = -10.328291781 + -2.583333334 Combine like terms: 2.583333334 + -2.583333334 = 0.000000000 0.000000000 + x = -10.328291781 + -2.583333334 x = -10.328291781 + -2.583333334 Combine like terms: -10.328291781 + -2.583333334 = -12.911625115 x = -12.911625115 Simplifying x = -12.911625115Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.744958447, -12.911625115}
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