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Simplifying 4 + 24x = 9x2 Solving 4 + 24x = 9x2 Solving for variable 'x'. Combine like terms: 9x2 + -9x2 = 0 4 + 24x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.4444444444 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + -2.666666667x + 0.4444444444 + x2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + -2.666666667x + x2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + -2.666666667x + x2 = 0 + 0.4444444444 -2.666666667x + x2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 -2.666666667x + x2 = 0.4444444444 The x term is -2.666666667x. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667x + 1.777777780 + x2 = 0.4444444444 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 0.4444444444 + 1.777777780 Combine like terms: 0.4444444444 + 1.777777780 = 2.2222222244 1.777777780 + -2.666666667x + x2 = 2.2222222244 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 2.2222222244 Calculate the square root of the right side: 1.490711986 Break this problem into two subproblems by setting (x + -1.333333334) equal to 1.490711986 and -1.490711986.Subproblem 1
x + -1.333333334 = 1.490711986 Simplifying x + -1.333333334 = 1.490711986 Reorder the terms: -1.333333334 + x = 1.490711986 Solving -1.333333334 + x = 1.490711986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = 1.490711986 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 1.490711986 + 1.333333334 x = 1.490711986 + 1.333333334 Combine like terms: 1.490711986 + 1.333333334 = 2.82404532 x = 2.82404532 Simplifying x = 2.82404532Subproblem 2
x + -1.333333334 = -1.490711986 Simplifying x + -1.333333334 = -1.490711986 Reorder the terms: -1.333333334 + x = -1.490711986 Solving -1.333333334 + x = -1.490711986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = -1.490711986 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -1.490711986 + 1.333333334 x = -1.490711986 + 1.333333334 Combine like terms: -1.490711986 + 1.333333334 = -0.157378652 x = -0.157378652 Simplifying x = -0.157378652Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.82404532, -0.157378652}
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