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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 = 4.9812578116 4.164931281 + 4.081632653x + x2 = 4.9812578116 Factor a perfect square on the left side: (x + 2.040816327)(x + 2.040816327) = 4.9812578116 Calculate the square root of the right side: 2.231873162 Break this problem into two subproblems by setting (x + 2.040816327) equal to 2.231873162 and -2.231873162.Subproblem 1
x + 2.040816327 = 2.231873162 Simplifying x + 2.040816327 = 2.231873162 Reorder the terms: 2.040816327 + x = 2.231873162 Solving 2.040816327 + x = 2.231873162 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 = 2.231873162 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + x = 2.231873162 + -2.040816327 x = 2.231873162 + -2.040816327 Combine like terms: 2.231873162 + -2.040816327 = 0.191056835 x = 0.191056835 Simplifying x = 0.191056835Subproblem 2
x + 2.040816327 = -2.231873162 Simplifying x + 2.040816327 = -2.231873162 Reorder the terms: 2.040816327 + x = -2.231873162 Solving 2.040816327 + x = -2.231873162 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 = -2.231873162 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + x = -2.231873162 + -2.040816327 x = -2.231873162 + -2.040816327 Combine like terms: -2.231873162 + -2.040816327 = -4.272689489 x = -4.272689489 Simplifying x = -4.272689489Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.191056835, -4.272689489}
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