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Simplifying 4.9x2 + 120x + -1000 = 0 Reorder the terms: -1000 + 120x + 4.9x2 = 0 Solving -1000 + 120x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -204.0816327 + 24.48979592x + x2 = 0 Move the constant term to the right: Add '204.0816327' to each side of the equation. -204.0816327 + 24.48979592x + 204.0816327 + x2 = 0 + 204.0816327 Reorder the terms: -204.0816327 + 204.0816327 + 24.48979592x + x2 = 0 + 204.0816327 Combine like terms: -204.0816327 + 204.0816327 = 0.0000000 0.0000000 + 24.48979592x + x2 = 0 + 204.0816327 24.48979592x + x2 = 0 + 204.0816327 Combine like terms: 0 + 204.0816327 = 204.0816327 24.48979592x + x2 = 204.0816327 The x term is 24.48979592x. Take half its coefficient (12.24489796). Square it (149.9375261) and add it to both sides. Add '149.9375261' to each side of the equation. 24.48979592x + 149.9375261 + x2 = 204.0816327 + 149.9375261 Reorder the terms: 149.9375261 + 24.48979592x + x2 = 204.0816327 + 149.9375261 Combine like terms: 204.0816327 + 149.9375261 = 354.0191588 149.9375261 + 24.48979592x + x2 = 354.0191588 Factor a perfect square on the left side: (x + 12.24489796)(x + 12.24489796) = 354.0191588 Calculate the square root of the right side: 18.815396855 Break this problem into two subproblems by setting (x + 12.24489796) equal to 18.815396855 and -18.815396855.Subproblem 1
x + 12.24489796 = 18.815396855 Simplifying x + 12.24489796 = 18.815396855 Reorder the terms: 12.24489796 + x = 18.815396855 Solving 12.24489796 + x = 18.815396855 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.24489796' to each side of the equation. 12.24489796 + -12.24489796 + x = 18.815396855 + -12.24489796 Combine like terms: 12.24489796 + -12.24489796 = 0.00000000 0.00000000 + x = 18.815396855 + -12.24489796 x = 18.815396855 + -12.24489796 Combine like terms: 18.815396855 + -12.24489796 = 6.570498895 x = 6.570498895 Simplifying x = 6.570498895Subproblem 2
x + 12.24489796 = -18.815396855 Simplifying x + 12.24489796 = -18.815396855 Reorder the terms: 12.24489796 + x = -18.815396855 Solving 12.24489796 + x = -18.815396855 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.24489796' to each side of the equation. 12.24489796 + -12.24489796 + x = -18.815396855 + -12.24489796 Combine like terms: 12.24489796 + -12.24489796 = 0.00000000 0.00000000 + x = -18.815396855 + -12.24489796 x = -18.815396855 + -12.24489796 Combine like terms: -18.815396855 + -12.24489796 = -31.060294815 x = -31.060294815 Simplifying x = -31.060294815Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.570498895, -31.060294815}
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