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Simplifying 9x2 + -24x + -5 = 0 Reorder the terms: -5 + -24x + 9x2 = 0 Solving -5 + -24x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.5555555556 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + -2.666666667x + 0.5555555556 + x2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + -2.666666667x + x2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + -2.666666667x + x2 = 0 + 0.5555555556 -2.666666667x + x2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 -2.666666667x + x2 = 0.5555555556 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 = 0.5555555556 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 0.5555555556 + 1.777777780 Combine like terms: 0.5555555556 + 1.777777780 = 2.3333333356 1.777777780 + -2.666666667x + x2 = 2.3333333356 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 2.3333333356 Calculate the square root of the right side: 1.527525232 Break this problem into two subproblems by setting (x + -1.333333334) equal to 1.527525232 and -1.527525232.Subproblem 1
x + -1.333333334 = 1.527525232 Simplifying x + -1.333333334 = 1.527525232 Reorder the terms: -1.333333334 + x = 1.527525232 Solving -1.333333334 + x = 1.527525232 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 = 1.527525232 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 1.527525232 + 1.333333334 x = 1.527525232 + 1.333333334 Combine like terms: 1.527525232 + 1.333333334 = 2.860858566 x = 2.860858566 Simplifying x = 2.860858566Subproblem 2
x + -1.333333334 = -1.527525232 Simplifying x + -1.333333334 = -1.527525232 Reorder the terms: -1.333333334 + x = -1.527525232 Solving -1.333333334 + x = -1.527525232 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 = -1.527525232 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -1.527525232 + 1.333333334 x = -1.527525232 + 1.333333334 Combine like terms: -1.527525232 + 1.333333334 = -0.194191898 x = -0.194191898 Simplifying x = -0.194191898Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.860858566, -0.194191898}
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