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Simplifying 0.25205x2 + 102.95x + 9500 = 0 Reorder the terms: 9500 + 102.95x + 0.25205x2 = 0 Solving 9500 + 102.95x + 0.25205x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.25205 the coefficient of the squared term: Divide each side by '0.25205'. 37690.93434 + 408.4507042x + x2 = 0 Move the constant term to the right: Add '-37690.93434' to each side of the equation. 37690.93434 + 408.4507042x + -37690.93434 + x2 = 0 + -37690.93434 Reorder the terms: 37690.93434 + -37690.93434 + 408.4507042x + x2 = 0 + -37690.93434 Combine like terms: 37690.93434 + -37690.93434 = 0.00000 0.00000 + 408.4507042x + x2 = 0 + -37690.93434 408.4507042x + x2 = 0 + -37690.93434 Combine like terms: 0 + -37690.93434 = -37690.93434 408.4507042x + x2 = -37690.93434 The x term is 408.4507042x. Take half its coefficient (204.2253521). Square it (41707.99444) and add it to both sides. Add '41707.99444' to each side of the equation. 408.4507042x + 41707.99444 + x2 = -37690.93434 + 41707.99444 Reorder the terms: 41707.99444 + 408.4507042x + x2 = -37690.93434 + 41707.99444 Combine like terms: -37690.93434 + 41707.99444 = 4017.0601 41707.99444 + 408.4507042x + x2 = 4017.0601 Factor a perfect square on the left side: (x + 204.2253521)(x + 204.2253521) = 4017.0601 Calculate the square root of the right side: 63.380281634 Break this problem into two subproblems by setting (x + 204.2253521) equal to 63.380281634 and -63.380281634.Subproblem 1
x + 204.2253521 = 63.380281634 Simplifying x + 204.2253521 = 63.380281634 Reorder the terms: 204.2253521 + x = 63.380281634 Solving 204.2253521 + x = 63.380281634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-204.2253521' to each side of the equation. 204.2253521 + -204.2253521 + x = 63.380281634 + -204.2253521 Combine like terms: 204.2253521 + -204.2253521 = 0.0000000 0.0000000 + x = 63.380281634 + -204.2253521 x = 63.380281634 + -204.2253521 Combine like terms: 63.380281634 + -204.2253521 = -140.845070466 x = -140.845070466 Simplifying x = -140.845070466Subproblem 2
x + 204.2253521 = -63.380281634 Simplifying x + 204.2253521 = -63.380281634 Reorder the terms: 204.2253521 + x = -63.380281634 Solving 204.2253521 + x = -63.380281634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-204.2253521' to each side of the equation. 204.2253521 + -204.2253521 + x = -63.380281634 + -204.2253521 Combine like terms: 204.2253521 + -204.2253521 = 0.0000000 0.0000000 + x = -63.380281634 + -204.2253521 x = -63.380281634 + -204.2253521 Combine like terms: -63.380281634 + -204.2253521 = -267.605633734 x = -267.605633734 Simplifying x = -267.605633734Solution
The solution to the problem is based on the solutions from the subproblems. x = {-140.845070466, -267.605633734}
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