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Simplifying -0.9x2 + -24x + 150 = 0 Reorder the terms: 150 + -24x + -0.9x2 = 0 Solving 150 + -24x + -0.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.9 the coefficient of the squared term: Divide each side by '-0.9'. -166.6666667 + 26.66666667x + x2 = 0 Move the constant term to the right: Add '166.6666667' to each side of the equation. -166.6666667 + 26.66666667x + 166.6666667 + x2 = 0 + 166.6666667 Reorder the terms: -166.6666667 + 166.6666667 + 26.66666667x + x2 = 0 + 166.6666667 Combine like terms: -166.6666667 + 166.6666667 = 0.0000000 0.0000000 + 26.66666667x + x2 = 0 + 166.6666667 26.66666667x + x2 = 0 + 166.6666667 Combine like terms: 0 + 166.6666667 = 166.6666667 26.66666667x + x2 = 166.6666667 The x term is 26.66666667x. Take half its coefficient (13.33333334). Square it (177.7777780) and add it to both sides. Add '177.7777780' to each side of the equation. 26.66666667x + 177.7777780 + x2 = 166.6666667 + 177.7777780 Reorder the terms: 177.7777780 + 26.66666667x + x2 = 166.6666667 + 177.7777780 Combine like terms: 166.6666667 + 177.7777780 = 344.4444447 177.7777780 + 26.66666667x + x2 = 344.4444447 Factor a perfect square on the left side: (x + 13.33333334)(x + 13.33333334) = 344.4444447 Calculate the square root of the right side: 18.55921455 Break this problem into two subproblems by setting (x + 13.33333334) equal to 18.55921455 and -18.55921455.Subproblem 1
x + 13.33333334 = 18.55921455 Simplifying x + 13.33333334 = 18.55921455 Reorder the terms: 13.33333334 + x = 18.55921455 Solving 13.33333334 + x = 18.55921455 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.33333334' to each side of the equation. 13.33333334 + -13.33333334 + x = 18.55921455 + -13.33333334 Combine like terms: 13.33333334 + -13.33333334 = 0.00000000 0.00000000 + x = 18.55921455 + -13.33333334 x = 18.55921455 + -13.33333334 Combine like terms: 18.55921455 + -13.33333334 = 5.22588121 x = 5.22588121 Simplifying x = 5.22588121Subproblem 2
x + 13.33333334 = -18.55921455 Simplifying x + 13.33333334 = -18.55921455 Reorder the terms: 13.33333334 + x = -18.55921455 Solving 13.33333334 + x = -18.55921455 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.33333334' to each side of the equation. 13.33333334 + -13.33333334 + x = -18.55921455 + -13.33333334 Combine like terms: 13.33333334 + -13.33333334 = 0.00000000 0.00000000 + x = -18.55921455 + -13.33333334 x = -18.55921455 + -13.33333334 Combine like terms: -18.55921455 + -13.33333334 = -31.89254789 x = -31.89254789 Simplifying x = -31.89254789Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.22588121, -31.89254789}
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