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Simplifying 0.49x2 + -5x + -5000 = 0 Reorder the terms: -5000 + -5x + 0.49x2 = 0 Solving -5000 + -5x + 0.49x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.49 the coefficient of the squared term: Divide each side by '0.49'. -10204.08163 + -10.20408163x + x2 = 0 Move the constant term to the right: Add '10204.08163' to each side of the equation. -10204.08163 + -10.20408163x + 10204.08163 + x2 = 0 + 10204.08163 Reorder the terms: -10204.08163 + 10204.08163 + -10.20408163x + x2 = 0 + 10204.08163 Combine like terms: -10204.08163 + 10204.08163 = 0.00000 0.00000 + -10.20408163x + x2 = 0 + 10204.08163 -10.20408163x + x2 = 0 + 10204.08163 Combine like terms: 0 + 10204.08163 = 10204.08163 -10.20408163x + x2 = 10204.08163 The x term is -10.20408163x. Take half its coefficient (-5.102040815). Square it (26.03082048) and add it to both sides. Add '26.03082048' to each side of the equation. -10.20408163x + 26.03082048 + x2 = 10204.08163 + 26.03082048 Reorder the terms: 26.03082048 + -10.20408163x + x2 = 10204.08163 + 26.03082048 Combine like terms: 10204.08163 + 26.03082048 = 10230.11245048 26.03082048 + -10.20408163x + x2 = 10230.11245048 Factor a perfect square on the left side: (x + -5.102040815)(x + -5.102040815) = 10230.11245048 Calculate the square root of the right side: 101.144018362 Break this problem into two subproblems by setting (x + -5.102040815) equal to 101.144018362 and -101.144018362.Subproblem 1
x + -5.102040815 = 101.144018362 Simplifying x + -5.102040815 = 101.144018362 Reorder the terms: -5.102040815 + x = 101.144018362 Solving -5.102040815 + x = 101.144018362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.102040815' to each side of the equation. -5.102040815 + 5.102040815 + x = 101.144018362 + 5.102040815 Combine like terms: -5.102040815 + 5.102040815 = 0.000000000 0.000000000 + x = 101.144018362 + 5.102040815 x = 101.144018362 + 5.102040815 Combine like terms: 101.144018362 + 5.102040815 = 106.246059177 x = 106.246059177 Simplifying x = 106.246059177Subproblem 2
x + -5.102040815 = -101.144018362 Simplifying x + -5.102040815 = -101.144018362 Reorder the terms: -5.102040815 + x = -101.144018362 Solving -5.102040815 + x = -101.144018362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.102040815' to each side of the equation. -5.102040815 + 5.102040815 + x = -101.144018362 + 5.102040815 Combine like terms: -5.102040815 + 5.102040815 = 0.000000000 0.000000000 + x = -101.144018362 + 5.102040815 x = -101.144018362 + 5.102040815 Combine like terms: -101.144018362 + 5.102040815 = -96.041977547 x = -96.041977547 Simplifying x = -96.041977547Solution
The solution to the problem is based on the solutions from the subproblems. x = {106.246059177, -96.041977547}
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