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Simplifying 0 = 4.9x2 + 20x + 1 Reorder the terms: 0 = 1 + 20x + 4.9x2 Solving 0 = 1 + 20x + 4.9x2 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + -20x + -4.9x2 = 1 + 20x + 4.9x2 + -1 + -20x + -4.9x2 Reorder the terms: -1 + -20x + -4.9x2 = 1 + -1 + 20x + -20x + 4.9x2 + -4.9x2 Combine like terms: 1 + -1 = 0 -1 + -20x + -4.9x2 = 0 + 20x + -20x + 4.9x2 + -4.9x2 -1 + -20x + -4.9x2 = 20x + -20x + 4.9x2 + -4.9x2 Combine like terms: 20x + -20x = 0 -1 + -20x + -4.9x2 = 0 + 4.9x2 + -4.9x2 -1 + -20x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 -1 + -20x + -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'. 0.2040816327 + 4.081632653x + x2 = 0 Move the constant term to the right: Add '-0.2040816327' to each side of the equation. 0.2040816327 + 4.081632653x + -0.2040816327 + x2 = 0 + -0.2040816327 Reorder the terms: 0.2040816327 + -0.2040816327 + 4.081632653x + x2 = 0 + -0.2040816327 Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000 0.0000000000 + 4.081632653x + x2 = 0 + -0.2040816327 4.081632653x + x2 = 0 + -0.2040816327 Combine like terms: 0 + -0.2040816327 = -0.2040816327 4.081632653x + x2 = -0.2040816327 The x term is 4.081632653x. Take half its coefficient (2.040816327). Square it (4.164931281) and add it to both sides. Add '4.164931281' to each side of the equation. 4.081632653x + 4.164931281 + x2 = -0.2040816327 + 4.164931281 Reorder the terms: 4.164931281 + 4.081632653x + x2 = -0.2040816327 + 4.164931281 Combine like terms: -0.2040816327 + 4.164931281 = 3.9608496483 4.164931281 + 4.081632653x + x2 = 3.9608496483 Factor a perfect square on the left side: (x + 2.040816327)(x + 2.040816327) = 3.9608496483 Calculate the square root of the right side: 1.990188345 Break this problem into two subproblems by setting (x + 2.040816327) equal to 1.990188345 and -1.990188345.Subproblem 1
x + 2.040816327 = 1.990188345 Simplifying x + 2.040816327 = 1.990188345 Reorder the terms: 2.040816327 + x = 1.990188345 Solving 2.040816327 + x = 1.990188345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.040816327' to each side of the equation. 2.040816327 + -2.040816327 + x = 1.990188345 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + x = 1.990188345 + -2.040816327 x = 1.990188345 + -2.040816327 Combine like terms: 1.990188345 + -2.040816327 = -0.050627982 x = -0.050627982 Simplifying x = -0.050627982Subproblem 2
x + 2.040816327 = -1.990188345 Simplifying x + 2.040816327 = -1.990188345 Reorder the terms: 2.040816327 + x = -1.990188345 Solving 2.040816327 + x = -1.990188345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.040816327' to each side of the equation. 2.040816327 + -2.040816327 + x = -1.990188345 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + x = -1.990188345 + -2.040816327 x = -1.990188345 + -2.040816327 Combine like terms: -1.990188345 + -2.040816327 = -4.031004672 x = -4.031004672 Simplifying x = -4.031004672Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.050627982, -4.031004672}
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