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Simplifying -4.9x2 + 20x + 1 = 5 Reorder the terms: 1 + 20x + -4.9x2 = 5 Solving 1 + 20x + -4.9x2 = 5 Solving for variable 'x'. Reorder the terms: 1 + -5 + 20x + -4.9x2 = 5 + -5 Combine like terms: 1 + -5 = -4 -4 + 20x + -4.9x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -4 + 20x + -4.9x2 = 0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 0.8163265306 + -4.081632653x + x2 = 0 Move the constant term to the right: Add '-0.8163265306' to each side of the equation. 0.8163265306 + -4.081632653x + -0.8163265306 + x2 = 0 + -0.8163265306 Reorder the terms: 0.8163265306 + -0.8163265306 + -4.081632653x + x2 = 0 + -0.8163265306 Combine like terms: 0.8163265306 + -0.8163265306 = 0.0000000000 0.0000000000 + -4.081632653x + x2 = 0 + -0.8163265306 -4.081632653x + x2 = 0 + -0.8163265306 Combine like terms: 0 + -0.8163265306 = -0.8163265306 -4.081632653x + x2 = -0.8163265306 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 = -0.8163265306 + 4.164931281 Reorder the terms: 4.164931281 + -4.081632653x + x2 = -0.8163265306 + 4.164931281 Combine like terms: -0.8163265306 + 4.164931281 = 3.3486047504 4.164931281 + -4.081632653x + x2 = 3.3486047504 Factor a perfect square on the left side: (x + -2.040816327)(x + -2.040816327) = 3.3486047504 Calculate the square root of the right side: 1.829919329 Break this problem into two subproblems by setting (x + -2.040816327) equal to 1.829919329 and -1.829919329.Subproblem 1
x + -2.040816327 = 1.829919329 Simplifying x + -2.040816327 = 1.829919329 Reorder the terms: -2.040816327 + x = 1.829919329 Solving -2.040816327 + x = 1.829919329 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 = 1.829919329 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + x = 1.829919329 + 2.040816327 x = 1.829919329 + 2.040816327 Combine like terms: 1.829919329 + 2.040816327 = 3.870735656 x = 3.870735656 Simplifying x = 3.870735656Subproblem 2
x + -2.040816327 = -1.829919329 Simplifying x + -2.040816327 = -1.829919329 Reorder the terms: -2.040816327 + x = -1.829919329 Solving -2.040816327 + x = -1.829919329 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 = -1.829919329 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + x = -1.829919329 + 2.040816327 x = -1.829919329 + 2.040816327 Combine like terms: -1.829919329 + 2.040816327 = 0.210896998 x = 0.210896998 Simplifying x = 0.210896998Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.870735656, 0.210896998}
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