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Simplifying 0 = 4.9x2 + 20x + -100 Reorder the terms: 0 = -100 + 20x + 4.9x2 Solving 0 = -100 + 20x + 4.9x2 Solving for variable 'x'. Combine like terms: 0 + 100 = 100 100 + -20x + -4.9x2 = -100 + 20x + 4.9x2 + 100 + -20x + -4.9x2 Reorder the terms: 100 + -20x + -4.9x2 = -100 + 100 + 20x + -20x + 4.9x2 + -4.9x2 Combine like terms: -100 + 100 = 0 100 + -20x + -4.9x2 = 0 + 20x + -20x + 4.9x2 + -4.9x2 100 + -20x + -4.9x2 = 20x + -20x + 4.9x2 + -4.9x2 Combine like terms: 20x + -20x = 0 100 + -20x + -4.9x2 = 0 + 4.9x2 + -4.9x2 100 + -20x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 100 + -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'. -20.40816327 + 4.081632653x + x2 = 0 Move the constant term to the right: Add '20.40816327' to each side of the equation. -20.40816327 + 4.081632653x + 20.40816327 + x2 = 0 + 20.40816327 Reorder the terms: -20.40816327 + 20.40816327 + 4.081632653x + x2 = 0 + 20.40816327 Combine like terms: -20.40816327 + 20.40816327 = 0.00000000 0.00000000 + 4.081632653x + x2 = 0 + 20.40816327 4.081632653x + x2 = 0 + 20.40816327 Combine like terms: 0 + 20.40816327 = 20.40816327 4.081632653x + x2 = 20.40816327 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 = 20.40816327 + 4.164931281 Reorder the terms: 4.164931281 + 4.081632653x + x2 = 20.40816327 + 4.164931281 Combine like terms: 20.40816327 + 4.164931281 = 24.573094551 4.164931281 + 4.081632653x + x2 = 24.573094551 Factor a perfect square on the left side: (x + 2.040816327)(x + 2.040816327) = 24.573094551 Calculate the square root of the right side: 4.957125634 Break this problem into two subproblems by setting (x + 2.040816327) equal to 4.957125634 and -4.957125634.Subproblem 1
x + 2.040816327 = 4.957125634 Simplifying x + 2.040816327 = 4.957125634 Reorder the terms: 2.040816327 + x = 4.957125634 Solving 2.040816327 + x = 4.957125634 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 = 4.957125634 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + x = 4.957125634 + -2.040816327 x = 4.957125634 + -2.040816327 Combine like terms: 4.957125634 + -2.040816327 = 2.916309307 x = 2.916309307 Simplifying x = 2.916309307Subproblem 2
x + 2.040816327 = -4.957125634 Simplifying x + 2.040816327 = -4.957125634 Reorder the terms: 2.040816327 + x = -4.957125634 Solving 2.040816327 + x = -4.957125634 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 = -4.957125634 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + x = -4.957125634 + -2.040816327 x = -4.957125634 + -2.040816327 Combine like terms: -4.957125634 + -2.040816327 = -6.997941961 x = -6.997941961 Simplifying x = -6.997941961Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.916309307, -6.997941961}
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