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Simplifying 0 = -4.9x2 + 25x + 2.45 Reorder the terms: 0 = 2.45 + 25x + -4.9x2 Solving 0 = 2.45 + 25x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -2.45 = -2.45 -2.45 + -25x + 4.9x2 = 2.45 + 25x + -4.9x2 + -2.45 + -25x + 4.9x2 Reorder the terms: -2.45 + -25x + 4.9x2 = 2.45 + -2.45 + 25x + -25x + -4.9x2 + 4.9x2 Combine like terms: 2.45 + -2.45 = 0.00 -2.45 + -25x + 4.9x2 = 0.00 + 25x + -25x + -4.9x2 + 4.9x2 -2.45 + -25x + 4.9x2 = 25x + -25x + -4.9x2 + 4.9x2 Combine like terms: 25x + -25x = 0 -2.45 + -25x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -2.45 + -25x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -2.45 + -25x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -0.5 + -5.102040816x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -5.102040816x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -5.102040816x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -5.102040816x + x2 = 0 + 0.5 -5.102040816x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -5.102040816x + x2 = 0.5 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 = 0.5 + 6.507705122 Reorder the terms: 6.507705122 + -5.102040816x + x2 = 0.5 + 6.507705122 Combine like terms: 0.5 + 6.507705122 = 7.007705122 6.507705122 + -5.102040816x + x2 = 7.007705122 Factor a perfect square on the left side: (x + -2.551020408)(x + -2.551020408) = 7.007705122 Calculate the square root of the right side: 2.647207042 Break this problem into two subproblems by setting (x + -2.551020408) equal to 2.647207042 and -2.647207042.Subproblem 1
x + -2.551020408 = 2.647207042 Simplifying x + -2.551020408 = 2.647207042 Reorder the terms: -2.551020408 + x = 2.647207042 Solving -2.551020408 + x = 2.647207042 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 = 2.647207042 + 2.551020408 Combine like terms: -2.551020408 + 2.551020408 = 0.000000000 0.000000000 + x = 2.647207042 + 2.551020408 x = 2.647207042 + 2.551020408 Combine like terms: 2.647207042 + 2.551020408 = 5.19822745 x = 5.19822745 Simplifying x = 5.19822745Subproblem 2
x + -2.551020408 = -2.647207042 Simplifying x + -2.551020408 = -2.647207042 Reorder the terms: -2.551020408 + x = -2.647207042 Solving -2.551020408 + x = -2.647207042 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 = -2.647207042 + 2.551020408 Combine like terms: -2.551020408 + 2.551020408 = 0.000000000 0.000000000 + x = -2.647207042 + 2.551020408 x = -2.647207042 + 2.551020408 Combine like terms: -2.647207042 + 2.551020408 = -0.096186634 x = -0.096186634 Simplifying x = -0.096186634Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.19822745, -0.096186634}
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