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Simplifying 9x2 = 4(6x + -1) Reorder the terms: 9x2 = 4(-1 + 6x) 9x2 = (-1 * 4 + 6x * 4) 9x2 = (-4 + 24x) Solving 9x2 = -4 + 24x Solving for variable 'x'. Reorder the terms: 4 + -24x + 9x2 = -4 + 24x + 4 + -24x Reorder the terms: 4 + -24x + 9x2 = -4 + 4 + 24x + -24x Combine like terms: -4 + 4 = 0 4 + -24x + 9x2 = 0 + 24x + -24x 4 + -24x + 9x2 = 24x + -24x Combine like terms: 24x + -24x = 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 = 1.3333333356 1.777777780 + -2.666666667x + x2 = 1.3333333356 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 1.3333333356 Calculate the square root of the right side: 1.154700539 Break this problem into two subproblems by setting (x + -1.333333334) equal to 1.154700539 and -1.154700539.Subproblem 1
x + -1.333333334 = 1.154700539 Simplifying x + -1.333333334 = 1.154700539 Reorder the terms: -1.333333334 + x = 1.154700539 Solving -1.333333334 + x = 1.154700539 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 = 1.154700539 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 1.154700539 + 1.333333334 x = 1.154700539 + 1.333333334 Combine like terms: 1.154700539 + 1.333333334 = 2.488033873 x = 2.488033873 Simplifying x = 2.488033873Subproblem 2
x + -1.333333334 = -1.154700539 Simplifying x + -1.333333334 = -1.154700539 Reorder the terms: -1.333333334 + x = -1.154700539 Solving -1.333333334 + x = -1.154700539 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 = -1.154700539 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -1.154700539 + 1.333333334 x = -1.154700539 + 1.333333334 Combine like terms: -1.154700539 + 1.333333334 = 0.178632795 x = 0.178632795 Simplifying x = 0.178632795Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.488033873, 0.178632795}
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