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Simplifying 4.9x2 + 25x + -100 = 0 Reorder the terms: -100 + 25x + 4.9x2 = 0 Solving -100 + 25x + 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'. -20.40816327 + 5.102040816x + x2 = 0 Move the constant term to the right: Add '20.40816327' to each side of the equation. -20.40816327 + 5.102040816x + 20.40816327 + x2 = 0 + 20.40816327 Reorder the terms: -20.40816327 + 20.40816327 + 5.102040816x + x2 = 0 + 20.40816327 Combine like terms: -20.40816327 + 20.40816327 = 0.00000000 0.00000000 + 5.102040816x + x2 = 0 + 20.40816327 5.102040816x + x2 = 0 + 20.40816327 Combine like terms: 0 + 20.40816327 = 20.40816327 5.102040816x + x2 = 20.40816327 The x term is 5.102040816x. Take half its coefficient (2.551020408). Square it (6.507705122) and add it to both sides. Add '6.507705122' to each side of the equation. 5.102040816x + 6.507705122 + x2 = 20.40816327 + 6.507705122 Reorder the terms: 6.507705122 + 5.102040816x + x2 = 20.40816327 + 6.507705122 Combine like terms: 20.40816327 + 6.507705122 = 26.915868392 6.507705122 + 5.102040816x + x2 = 26.915868392 Factor a perfect square on the left side: (x + 2.551020408)(x + 2.551020408) = 26.915868392 Calculate the square root of the right side: 5.188050539 Break this problem into two subproblems by setting (x + 2.551020408) equal to 5.188050539 and -5.188050539.Subproblem 1
x + 2.551020408 = 5.188050539 Simplifying x + 2.551020408 = 5.188050539 Reorder the terms: 2.551020408 + x = 5.188050539 Solving 2.551020408 + x = 5.188050539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.551020408' to each side of the equation. 2.551020408 + -2.551020408 + x = 5.188050539 + -2.551020408 Combine like terms: 2.551020408 + -2.551020408 = 0.000000000 0.000000000 + x = 5.188050539 + -2.551020408 x = 5.188050539 + -2.551020408 Combine like terms: 5.188050539 + -2.551020408 = 2.637030131 x = 2.637030131 Simplifying x = 2.637030131Subproblem 2
x + 2.551020408 = -5.188050539 Simplifying x + 2.551020408 = -5.188050539 Reorder the terms: 2.551020408 + x = -5.188050539 Solving 2.551020408 + x = -5.188050539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.551020408' to each side of the equation. 2.551020408 + -2.551020408 + x = -5.188050539 + -2.551020408 Combine like terms: 2.551020408 + -2.551020408 = 0.000000000 0.000000000 + x = -5.188050539 + -2.551020408 x = -5.188050539 + -2.551020408 Combine like terms: -5.188050539 + -2.551020408 = -7.739070947 x = -7.739070947 Simplifying x = -7.739070947Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.637030131, -7.739070947}
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