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Simplifying 4.9x2 + 1.7x + -50 = 0 Reorder the terms: -50 + 1.7x + 4.9x2 = 0 Solving -50 + 1.7x + 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'. -10.20408163 + 0.3469387755x + x2 = 0 Move the constant term to the right: Add '10.20408163' to each side of the equation. -10.20408163 + 0.3469387755x + 10.20408163 + x2 = 0 + 10.20408163 Reorder the terms: -10.20408163 + 10.20408163 + 0.3469387755x + x2 = 0 + 10.20408163 Combine like terms: -10.20408163 + 10.20408163 = 0.00000000 0.00000000 + 0.3469387755x + x2 = 0 + 10.20408163 0.3469387755x + x2 = 0 + 10.20408163 Combine like terms: 0 + 10.20408163 = 10.20408163 0.3469387755x + x2 = 10.20408163 The x term is 0.3469387755x. Take half its coefficient (0.1734693878). Square it (0.03009162850) and add it to both sides. Add '0.03009162850' to each side of the equation. 0.3469387755x + 0.03009162850 + x2 = 10.20408163 + 0.03009162850 Reorder the terms: 0.03009162850 + 0.3469387755x + x2 = 10.20408163 + 0.03009162850 Combine like terms: 10.20408163 + 0.03009162850 = 10.2341732585 0.03009162850 + 0.3469387755x + x2 = 10.2341732585 Factor a perfect square on the left side: (x + 0.1734693878)(x + 0.1734693878) = 10.2341732585 Calculate the square root of the right side: 3.199089442 Break this problem into two subproblems by setting (x + 0.1734693878) equal to 3.199089442 and -3.199089442.Subproblem 1
x + 0.1734693878 = 3.199089442 Simplifying x + 0.1734693878 = 3.199089442 Reorder the terms: 0.1734693878 + x = 3.199089442 Solving 0.1734693878 + x = 3.199089442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1734693878' to each side of the equation. 0.1734693878 + -0.1734693878 + x = 3.199089442 + -0.1734693878 Combine like terms: 0.1734693878 + -0.1734693878 = 0.0000000000 0.0000000000 + x = 3.199089442 + -0.1734693878 x = 3.199089442 + -0.1734693878 Combine like terms: 3.199089442 + -0.1734693878 = 3.0256200542 x = 3.0256200542 Simplifying x = 3.0256200542Subproblem 2
x + 0.1734693878 = -3.199089442 Simplifying x + 0.1734693878 = -3.199089442 Reorder the terms: 0.1734693878 + x = -3.199089442 Solving 0.1734693878 + x = -3.199089442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1734693878' to each side of the equation. 0.1734693878 + -0.1734693878 + x = -3.199089442 + -0.1734693878 Combine like terms: 0.1734693878 + -0.1734693878 = 0.0000000000 0.0000000000 + x = -3.199089442 + -0.1734693878 x = -3.199089442 + -0.1734693878 Combine like terms: -3.199089442 + -0.1734693878 = -3.3725588298 x = -3.3725588298 Simplifying x = -3.3725588298Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.0256200542, -3.3725588298}
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