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Simplifying 52x2 + 5x + -100 = 0 Reorder the terms: -100 + 5x + 52x2 = 0 Solving -100 + 5x + 52x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 52 the coefficient of the squared term: Divide each side by '52'. -1.923076923 + 0.09615384615x + x2 = 0 Move the constant term to the right: Add '1.923076923' to each side of the equation. -1.923076923 + 0.09615384615x + 1.923076923 + x2 = 0 + 1.923076923 Reorder the terms: -1.923076923 + 1.923076923 + 0.09615384615x + x2 = 0 + 1.923076923 Combine like terms: -1.923076923 + 1.923076923 = 0.000000000 0.000000000 + 0.09615384615x + x2 = 0 + 1.923076923 0.09615384615x + x2 = 0 + 1.923076923 Combine like terms: 0 + 1.923076923 = 1.923076923 0.09615384615x + x2 = 1.923076923 The x term is 0.09615384615x. Take half its coefficient (0.04807692308). Square it (0.002311390533) and add it to both sides. Add '0.002311390533' to each side of the equation. 0.09615384615x + 0.002311390533 + x2 = 1.923076923 + 0.002311390533 Reorder the terms: 0.002311390533 + 0.09615384615x + x2 = 1.923076923 + 0.002311390533 Combine like terms: 1.923076923 + 0.002311390533 = 1.925388313533 0.002311390533 + 0.09615384615x + x2 = 1.925388313533 Factor a perfect square on the left side: (x + 0.04807692308)(x + 0.04807692308) = 1.925388313533 Calculate the square root of the right side: 1.387583624 Break this problem into two subproblems by setting (x + 0.04807692308) equal to 1.387583624 and -1.387583624.Subproblem 1
x + 0.04807692308 = 1.387583624 Simplifying x + 0.04807692308 = 1.387583624 Reorder the terms: 0.04807692308 + x = 1.387583624 Solving 0.04807692308 + x = 1.387583624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04807692308' to each side of the equation. 0.04807692308 + -0.04807692308 + x = 1.387583624 + -0.04807692308 Combine like terms: 0.04807692308 + -0.04807692308 = 0.00000000000 0.00000000000 + x = 1.387583624 + -0.04807692308 x = 1.387583624 + -0.04807692308 Combine like terms: 1.387583624 + -0.04807692308 = 1.33950670092 x = 1.33950670092 Simplifying x = 1.33950670092Subproblem 2
x + 0.04807692308 = -1.387583624 Simplifying x + 0.04807692308 = -1.387583624 Reorder the terms: 0.04807692308 + x = -1.387583624 Solving 0.04807692308 + x = -1.387583624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04807692308' to each side of the equation. 0.04807692308 + -0.04807692308 + x = -1.387583624 + -0.04807692308 Combine like terms: 0.04807692308 + -0.04807692308 = 0.00000000000 0.00000000000 + x = -1.387583624 + -0.04807692308 x = -1.387583624 + -0.04807692308 Combine like terms: -1.387583624 + -0.04807692308 = -1.43566054708 x = -1.43566054708 Simplifying x = -1.43566054708Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.33950670092, -1.43566054708}
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