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Simplifying (5x2 + -4x + -24) + (5x2 + 9x) = 0 Reorder the terms: (-24 + -4x + 5x2) + (5x2 + 9x) = 0 Remove parenthesis around (-24 + -4x + 5x2) -24 + -4x + 5x2 + (5x2 + 9x) = 0 Reorder the terms: -24 + -4x + 5x2 + (9x + 5x2) = 0 Remove parenthesis around (9x + 5x2) -24 + -4x + 5x2 + 9x + 5x2 = 0 Reorder the terms: -24 + -4x + 9x + 5x2 + 5x2 = 0 Combine like terms: -4x + 9x = 5x -24 + 5x + 5x2 + 5x2 = 0 Combine like terms: 5x2 + 5x2 = 10x2 -24 + 5x + 10x2 = 0 Solving -24 + 5x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2.4 + 0.5x + x2 = 0.0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + 0.5x + 2.4 + x2 = 0.0 + 2.4 Reorder the terms: -2.4 + 2.4 + 0.5x + x2 = 0.0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + 0.5x + x2 = 0.0 + 2.4 0.5x + x2 = 0.0 + 2.4 Combine like terms: 0.0 + 2.4 = 2.4 0.5x + x2 = 2.4 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 2.4 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 2.4 + 0.0625 Combine like terms: 2.4 + 0.0625 = 2.4625 0.0625 + 0.5x + x2 = 2.4625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 2.4625 Calculate the square root of the right side: 1.569235483 Break this problem into two subproblems by setting (x + 0.25) equal to 1.569235483 and -1.569235483.Subproblem 1
x + 0.25 = 1.569235483 Simplifying x + 0.25 = 1.569235483 Reorder the terms: 0.25 + x = 1.569235483 Solving 0.25 + x = 1.569235483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.569235483 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.569235483 + -0.25 x = 1.569235483 + -0.25 Combine like terms: 1.569235483 + -0.25 = 1.319235483 x = 1.319235483 Simplifying x = 1.319235483Subproblem 2
x + 0.25 = -1.569235483 Simplifying x + 0.25 = -1.569235483 Reorder the terms: 0.25 + x = -1.569235483 Solving 0.25 + x = -1.569235483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.569235483 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.569235483 + -0.25 x = -1.569235483 + -0.25 Combine like terms: -1.569235483 + -0.25 = -1.819235483 x = -1.819235483 Simplifying x = -1.819235483Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.319235483, -1.819235483}
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