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Simplifying 0 = 4.9x2 + 20x + -300 Reorder the terms: 0 = -300 + 20x + 4.9x2 Solving 0 = -300 + 20x + 4.9x2 Solving for variable 'x'. Combine like terms: 0 + 300 = 300 300 + -20x + -4.9x2 = -300 + 20x + 4.9x2 + 300 + -20x + -4.9x2 Reorder the terms: 300 + -20x + -4.9x2 = -300 + 300 + 20x + -20x + 4.9x2 + -4.9x2 Combine like terms: -300 + 300 = 0 300 + -20x + -4.9x2 = 0 + 20x + -20x + 4.9x2 + -4.9x2 300 + -20x + -4.9x2 = 20x + -20x + 4.9x2 + -4.9x2 Combine like terms: 20x + -20x = 0 300 + -20x + -4.9x2 = 0 + 4.9x2 + -4.9x2 300 + -20x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 300 + -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'. -61.2244898 + 4.081632653x + x2 = 0 Move the constant term to the right: Add '61.2244898' to each side of the equation. -61.2244898 + 4.081632653x + 61.2244898 + x2 = 0 + 61.2244898 Reorder the terms: -61.2244898 + 61.2244898 + 4.081632653x + x2 = 0 + 61.2244898 Combine like terms: -61.2244898 + 61.2244898 = 0.0000000 0.0000000 + 4.081632653x + x2 = 0 + 61.2244898 4.081632653x + x2 = 0 + 61.2244898 Combine like terms: 0 + 61.2244898 = 61.2244898 4.081632653x + x2 = 61.2244898 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 = 61.2244898 + 4.164931281 Reorder the terms: 4.164931281 + 4.081632653x + x2 = 61.2244898 + 4.164931281 Combine like terms: 61.2244898 + 4.164931281 = 65.389421081 4.164931281 + 4.081632653x + x2 = 65.389421081 Factor a perfect square on the left side: (x + 2.040816327)(x + 2.040816327) = 65.389421081 Calculate the square root of the right side: 8.086372554 Break this problem into two subproblems by setting (x + 2.040816327) equal to 8.086372554 and -8.086372554.Subproblem 1
x + 2.040816327 = 8.086372554 Simplifying x + 2.040816327 = 8.086372554 Reorder the terms: 2.040816327 + x = 8.086372554 Solving 2.040816327 + x = 8.086372554 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 = 8.086372554 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + x = 8.086372554 + -2.040816327 x = 8.086372554 + -2.040816327 Combine like terms: 8.086372554 + -2.040816327 = 6.045556227 x = 6.045556227 Simplifying x = 6.045556227Subproblem 2
x + 2.040816327 = -8.086372554 Simplifying x + 2.040816327 = -8.086372554 Reorder the terms: 2.040816327 + x = -8.086372554 Solving 2.040816327 + x = -8.086372554 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 = -8.086372554 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + x = -8.086372554 + -2.040816327 x = -8.086372554 + -2.040816327 Combine like terms: -8.086372554 + -2.040816327 = -10.127188881 x = -10.127188881 Simplifying x = -10.127188881Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.045556227, -10.127188881}
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