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Simplifying -9x2 + -5x + 24 = 0 Reorder the terms: 24 + -5x + -9x2 = 0 Solving 24 + -5x + -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'. -2.666666667 + 0.5555555556x + x2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + 0.5555555556x + 2.666666667 + x2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + 0.5555555556x + x2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + 0.5555555556x + x2 = 0 + 2.666666667 0.5555555556x + x2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 0.5555555556x + x2 = 2.666666667 The x term is 0.5555555556x. Take half its coefficient (0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. 0.5555555556x + 0.07716049384 + x2 = 2.666666667 + 0.07716049384 Reorder the terms: 0.07716049384 + 0.5555555556x + x2 = 2.666666667 + 0.07716049384 Combine like terms: 2.666666667 + 0.07716049384 = 2.74382716084 0.07716049384 + 0.5555555556x + x2 = 2.74382716084 Factor a perfect square on the left side: (x + 0.2777777778)(x + 0.2777777778) = 2.74382716084 Calculate the square root of the right side: 1.656450169 Break this problem into two subproblems by setting (x + 0.2777777778) equal to 1.656450169 and -1.656450169.Subproblem 1
x + 0.2777777778 = 1.656450169 Simplifying x + 0.2777777778 = 1.656450169 Reorder the terms: 0.2777777778 + x = 1.656450169 Solving 0.2777777778 + x = 1.656450169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = 1.656450169 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = 1.656450169 + -0.2777777778 x = 1.656450169 + -0.2777777778 Combine like terms: 1.656450169 + -0.2777777778 = 1.3786723912 x = 1.3786723912 Simplifying x = 1.3786723912Subproblem 2
x + 0.2777777778 = -1.656450169 Simplifying x + 0.2777777778 = -1.656450169 Reorder the terms: 0.2777777778 + x = -1.656450169 Solving 0.2777777778 + x = -1.656450169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = -1.656450169 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = -1.656450169 + -0.2777777778 x = -1.656450169 + -0.2777777778 Combine like terms: -1.656450169 + -0.2777777778 = -1.9342279468 x = -1.9342279468 Simplifying x = -1.9342279468Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3786723912, -1.9342279468}
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