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Simplifying 25x + -3x2 = 18 Solving 25x + -3x2 = 18 Solving for variable 'x'. Reorder the terms: -18 + 25x + -3x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + 25x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 6 + -8.333333333x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -8.333333333x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -8.333333333x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -8.333333333x + x2 = 0 + -6 -8.333333333x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -8.333333333x + x2 = -6 The x term is -8.333333333x. Take half its coefficient (-4.166666667). Square it (17.36111111) and add it to both sides. Add '17.36111111' to each side of the equation. -8.333333333x + 17.36111111 + x2 = -6 + 17.36111111 Reorder the terms: 17.36111111 + -8.333333333x + x2 = -6 + 17.36111111 Combine like terms: -6 + 17.36111111 = 11.36111111 17.36111111 + -8.333333333x + x2 = 11.36111111 Factor a perfect square on the left side: (x + -4.166666667)(x + -4.166666667) = 11.36111111 Calculate the square root of the right side: 3.370624736 Break this problem into two subproblems by setting (x + -4.166666667) equal to 3.370624736 and -3.370624736.Subproblem 1
x + -4.166666667 = 3.370624736 Simplifying x + -4.166666667 = 3.370624736 Reorder the terms: -4.166666667 + x = 3.370624736 Solving -4.166666667 + x = 3.370624736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.166666667' to each side of the equation. -4.166666667 + 4.166666667 + x = 3.370624736 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + x = 3.370624736 + 4.166666667 x = 3.370624736 + 4.166666667 Combine like terms: 3.370624736 + 4.166666667 = 7.537291403 x = 7.537291403 Simplifying x = 7.537291403Subproblem 2
x + -4.166666667 = -3.370624736 Simplifying x + -4.166666667 = -3.370624736 Reorder the terms: -4.166666667 + x = -3.370624736 Solving -4.166666667 + x = -3.370624736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.166666667' to each side of the equation. -4.166666667 + 4.166666667 + x = -3.370624736 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + x = -3.370624736 + 4.166666667 x = -3.370624736 + 4.166666667 Combine like terms: -3.370624736 + 4.166666667 = 0.796041931 x = 0.796041931 Simplifying x = 0.796041931Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.537291403, 0.796041931}
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