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Simplifying -53x + 95 = 5x2 + -9 Reorder the terms: 95 + -53x = 5x2 + -9 Reorder the terms: 95 + -53x = -9 + 5x2 Solving 95 + -53x = -9 + 5x2 Solving for variable 'x'. Reorder the terms: 95 + 9 + -53x + -5x2 = -9 + 5x2 + 9 + -5x2 Combine like terms: 95 + 9 = 104 104 + -53x + -5x2 = -9 + 5x2 + 9 + -5x2 Reorder the terms: 104 + -53x + -5x2 = -9 + 9 + 5x2 + -5x2 Combine like terms: -9 + 9 = 0 104 + -53x + -5x2 = 0 + 5x2 + -5x2 104 + -53x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 104 + -53x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -20.8 + 10.6x + x2 = 0 Move the constant term to the right: Add '20.8' to each side of the equation. -20.8 + 10.6x + 20.8 + x2 = 0 + 20.8 Reorder the terms: -20.8 + 20.8 + 10.6x + x2 = 0 + 20.8 Combine like terms: -20.8 + 20.8 = 0.0 0.0 + 10.6x + x2 = 0 + 20.8 10.6x + x2 = 0 + 20.8 Combine like terms: 0 + 20.8 = 20.8 10.6x + x2 = 20.8 The x term is 10.6x. Take half its coefficient (5.3). Square it (28.09) and add it to both sides. Add '28.09' to each side of the equation. 10.6x + 28.09 + x2 = 20.8 + 28.09 Reorder the terms: 28.09 + 10.6x + x2 = 20.8 + 28.09 Combine like terms: 20.8 + 28.09 = 48.89 28.09 + 10.6x + x2 = 48.89 Factor a perfect square on the left side: (x + 5.3)(x + 5.3) = 48.89 Calculate the square root of the right side: 6.992138443 Break this problem into two subproblems by setting (x + 5.3) equal to 6.992138443 and -6.992138443.Subproblem 1
x + 5.3 = 6.992138443 Simplifying x + 5.3 = 6.992138443 Reorder the terms: 5.3 + x = 6.992138443 Solving 5.3 + x = 6.992138443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.3' to each side of the equation. 5.3 + -5.3 + x = 6.992138443 + -5.3 Combine like terms: 5.3 + -5.3 = 0.0 0.0 + x = 6.992138443 + -5.3 x = 6.992138443 + -5.3 Combine like terms: 6.992138443 + -5.3 = 1.692138443 x = 1.692138443 Simplifying x = 1.692138443Subproblem 2
x + 5.3 = -6.992138443 Simplifying x + 5.3 = -6.992138443 Reorder the terms: 5.3 + x = -6.992138443 Solving 5.3 + x = -6.992138443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.3' to each side of the equation. 5.3 + -5.3 + x = -6.992138443 + -5.3 Combine like terms: 5.3 + -5.3 = 0.0 0.0 + x = -6.992138443 + -5.3 x = -6.992138443 + -5.3 Combine like terms: -6.992138443 + -5.3 = -12.292138443 x = -12.292138443 Simplifying x = -12.292138443Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.692138443, -12.292138443}
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