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Simplifying 5x2 + -48x + -100 = 0 Reorder the terms: -100 + -48x + 5x2 = 0 Solving -100 + -48x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -20 + -9.6x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -9.6x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -9.6x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -9.6x + x2 = 0 + 20 -9.6x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -9.6x + x2 = 20 The x term is -9.6x. Take half its coefficient (-4.8). Square it (23.04) and add it to both sides. Add '23.04' to each side of the equation. -9.6x + 23.04 + x2 = 20 + 23.04 Reorder the terms: 23.04 + -9.6x + x2 = 20 + 23.04 Combine like terms: 20 + 23.04 = 43.04 23.04 + -9.6x + x2 = 43.04 Factor a perfect square on the left side: (x + -4.8)(x + -4.8) = 43.04 Calculate the square root of the right side: 6.560487787 Break this problem into two subproblems by setting (x + -4.8) equal to 6.560487787 and -6.560487787.Subproblem 1
x + -4.8 = 6.560487787 Simplifying x + -4.8 = 6.560487787 Reorder the terms: -4.8 + x = 6.560487787 Solving -4.8 + x = 6.560487787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.8' to each side of the equation. -4.8 + 4.8 + x = 6.560487787 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + x = 6.560487787 + 4.8 x = 6.560487787 + 4.8 Combine like terms: 6.560487787 + 4.8 = 11.360487787 x = 11.360487787 Simplifying x = 11.360487787Subproblem 2
x + -4.8 = -6.560487787 Simplifying x + -4.8 = -6.560487787 Reorder the terms: -4.8 + x = -6.560487787 Solving -4.8 + x = -6.560487787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.8' to each side of the equation. -4.8 + 4.8 + x = -6.560487787 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + x = -6.560487787 + 4.8 x = -6.560487787 + 4.8 Combine like terms: -6.560487787 + 4.8 = -1.760487787 x = -1.760487787 Simplifying x = -1.760487787Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.360487787, -1.760487787}
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