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Simplifying 42 = 20x + 4.9x2 Solving 42 = 20x + 4.9x2 Solving for variable 'x'. Reorder the terms: 42 + -20x + -4.9x2 = 20x + -20x + 4.9x2 + -4.9x2 Combine like terms: 20x + -20x = 0 42 + -20x + -4.9x2 = 0 + 4.9x2 + -4.9x2 42 + -20x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 42 + -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'. -8.571428571 + 4.081632653x + x2 = 0 Move the constant term to the right: Add '8.571428571' to each side of the equation. -8.571428571 + 4.081632653x + 8.571428571 + x2 = 0 + 8.571428571 Reorder the terms: -8.571428571 + 8.571428571 + 4.081632653x + x2 = 0 + 8.571428571 Combine like terms: -8.571428571 + 8.571428571 = 0.000000000 0.000000000 + 4.081632653x + x2 = 0 + 8.571428571 4.081632653x + x2 = 0 + 8.571428571 Combine like terms: 0 + 8.571428571 = 8.571428571 4.081632653x + x2 = 8.571428571 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 = 8.571428571 + 4.164931281 Reorder the terms: 4.164931281 + 4.081632653x + x2 = 8.571428571 + 4.164931281 Combine like terms: 8.571428571 + 4.164931281 = 12.736359852 4.164931281 + 4.081632653x + x2 = 12.736359852 Factor a perfect square on the left side: (x + 2.040816327)(x + 2.040816327) = 12.736359852 Calculate the square root of the right side: 3.5688037 Break this problem into two subproblems by setting (x + 2.040816327) equal to 3.5688037 and -3.5688037.Subproblem 1
x + 2.040816327 = 3.5688037 Simplifying x + 2.040816327 = 3.5688037 Reorder the terms: 2.040816327 + x = 3.5688037 Solving 2.040816327 + x = 3.5688037 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 = 3.5688037 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + x = 3.5688037 + -2.040816327 x = 3.5688037 + -2.040816327 Combine like terms: 3.5688037 + -2.040816327 = 1.527987373 x = 1.527987373 Simplifying x = 1.527987373Subproblem 2
x + 2.040816327 = -3.5688037 Simplifying x + 2.040816327 = -3.5688037 Reorder the terms: 2.040816327 + x = -3.5688037 Solving 2.040816327 + x = -3.5688037 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 = -3.5688037 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + x = -3.5688037 + -2.040816327 x = -3.5688037 + -2.040816327 Combine like terms: -3.5688037 + -2.040816327 = -5.609620027 x = -5.609620027 Simplifying x = -5.609620027Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.527987373, -5.609620027}
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