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Simplifying 4 = 4.9x2 + 20x + 1 Reorder the terms: 4 = 1 + 20x + 4.9x2 Solving 4 = 1 + 20x + 4.9x2 Solving for variable 'x'. Combine like terms: 4 + -1 = 3 3 + -20x + -4.9x2 = 1 + 20x + 4.9x2 + -1 + -20x + -4.9x2 Reorder the terms: 3 + -20x + -4.9x2 = 1 + -1 + 20x + -20x + 4.9x2 + -4.9x2 Combine like terms: 1 + -1 = 0 3 + -20x + -4.9x2 = 0 + 20x + -20x + 4.9x2 + -4.9x2 3 + -20x + -4.9x2 = 20x + -20x + 4.9x2 + -4.9x2 Combine like terms: 20x + -20x = 0 3 + -20x + -4.9x2 = 0 + 4.9x2 + -4.9x2 3 + -20x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 3 + -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'. -0.612244898 + 4.081632653x + x2 = 0 Move the constant term to the right: Add '0.612244898' to each side of the equation. -0.612244898 + 4.081632653x + 0.612244898 + x2 = 0 + 0.612244898 Reorder the terms: -0.612244898 + 0.612244898 + 4.081632653x + x2 = 0 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + 4.081632653x + x2 = 0 + 0.612244898 4.081632653x + x2 = 0 + 0.612244898 Combine like terms: 0 + 0.612244898 = 0.612244898 4.081632653x + x2 = 0.612244898 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 = 0.612244898 + 4.164931281 Reorder the terms: 4.164931281 + 4.081632653x + x2 = 0.612244898 + 4.164931281 Combine like terms: 0.612244898 + 4.164931281 = 4.777176179 4.164931281 + 4.081632653x + x2 = 4.777176179 Factor a perfect square on the left side: (x + 2.040816327)(x + 2.040816327) = 4.777176179 Calculate the square root of the right side: 2.185675223 Break this problem into two subproblems by setting (x + 2.040816327) equal to 2.185675223 and -2.185675223.Subproblem 1
x + 2.040816327 = 2.185675223 Simplifying x + 2.040816327 = 2.185675223 Reorder the terms: 2.040816327 + x = 2.185675223 Solving 2.040816327 + x = 2.185675223 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 = 2.185675223 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + x = 2.185675223 + -2.040816327 x = 2.185675223 + -2.040816327 Combine like terms: 2.185675223 + -2.040816327 = 0.144858896 x = 0.144858896 Simplifying x = 0.144858896Subproblem 2
x + 2.040816327 = -2.185675223 Simplifying x + 2.040816327 = -2.185675223 Reorder the terms: 2.040816327 + x = -2.185675223 Solving 2.040816327 + x = -2.185675223 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 = -2.185675223 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + x = -2.185675223 + -2.040816327 x = -2.185675223 + -2.040816327 Combine like terms: -2.185675223 + -2.040816327 = -4.22649155 x = -4.22649155 Simplifying x = -4.22649155Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.144858896, -4.22649155}
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