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Simplifying x = -5x2 + 460x + 35 Reorder the terms: x = 35 + 460x + -5x2 Solving x = 35 + 460x + -5x2 Solving for variable 'x'. Reorder the terms: -35 + x + -460x + 5x2 = 35 + 460x + -5x2 + -35 + -460x + 5x2 Combine like terms: x + -460x = -459x -35 + -459x + 5x2 = 35 + 460x + -5x2 + -35 + -460x + 5x2 Reorder the terms: -35 + -459x + 5x2 = 35 + -35 + 460x + -460x + -5x2 + 5x2 Combine like terms: 35 + -35 = 0 -35 + -459x + 5x2 = 0 + 460x + -460x + -5x2 + 5x2 -35 + -459x + 5x2 = 460x + -460x + -5x2 + 5x2 Combine like terms: 460x + -460x = 0 -35 + -459x + 5x2 = 0 + -5x2 + 5x2 -35 + -459x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -35 + -459x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7 + -91.8x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -91.8x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -91.8x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -91.8x + x2 = 0 + 7 -91.8x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -91.8x + x2 = 7 The x term is -91.8x. Take half its coefficient (-45.9). Square it (2106.81) and add it to both sides. Add '2106.81' to each side of the equation. -91.8x + 2106.81 + x2 = 7 + 2106.81 Reorder the terms: 2106.81 + -91.8x + x2 = 7 + 2106.81 Combine like terms: 7 + 2106.81 = 2113.81 2106.81 + -91.8x + x2 = 2113.81 Factor a perfect square on the left side: (x + -45.9)(x + -45.9) = 2113.81 Calculate the square root of the right side: 45.97618949 Break this problem into two subproblems by setting (x + -45.9) equal to 45.97618949 and -45.97618949.Subproblem 1
x + -45.9 = 45.97618949 Simplifying x + -45.9 = 45.97618949 Reorder the terms: -45.9 + x = 45.97618949 Solving -45.9 + x = 45.97618949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45.9' to each side of the equation. -45.9 + 45.9 + x = 45.97618949 + 45.9 Combine like terms: -45.9 + 45.9 = 0.0 0.0 + x = 45.97618949 + 45.9 x = 45.97618949 + 45.9 Combine like terms: 45.97618949 + 45.9 = 91.87618949 x = 91.87618949 Simplifying x = 91.87618949Subproblem 2
x + -45.9 = -45.97618949 Simplifying x + -45.9 = -45.97618949 Reorder the terms: -45.9 + x = -45.97618949 Solving -45.9 + x = -45.97618949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45.9' to each side of the equation. -45.9 + 45.9 + x = -45.97618949 + 45.9 Combine like terms: -45.9 + 45.9 = 0.0 0.0 + x = -45.97618949 + 45.9 x = -45.97618949 + 45.9 Combine like terms: -45.97618949 + 45.9 = -0.07618949 x = -0.07618949 Simplifying x = -0.07618949Solution
The solution to the problem is based on the solutions from the subproblems. x = {91.87618949, -0.07618949}
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