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Simplifying 4.9x2 + -14x + -76 = 0 Reorder the terms: -76 + -14x + 4.9x2 = 0 Solving -76 + -14x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -15.51020408 + -2.857142857x + x2 = 0 Move the constant term to the right: Add '15.51020408' to each side of the equation. -15.51020408 + -2.857142857x + 15.51020408 + x2 = 0 + 15.51020408 Reorder the terms: -15.51020408 + 15.51020408 + -2.857142857x + x2 = 0 + 15.51020408 Combine like terms: -15.51020408 + 15.51020408 = 0.00000000 0.00000000 + -2.857142857x + x2 = 0 + 15.51020408 -2.857142857x + x2 = 0 + 15.51020408 Combine like terms: 0 + 15.51020408 = 15.51020408 -2.857142857x + x2 = 15.51020408 The x term is -2.857142857x. Take half its coefficient (-1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. -2.857142857x + 2.040816328 + x2 = 15.51020408 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857x + x2 = 15.51020408 + 2.040816328 Combine like terms: 15.51020408 + 2.040816328 = 17.551020408 2.040816328 + -2.857142857x + x2 = 17.551020408 Factor a perfect square on the left side: (x + -1.428571429)(x + -1.428571429) = 17.551020408 Calculate the square root of the right side: 4.1893938 Break this problem into two subproblems by setting (x + -1.428571429) equal to 4.1893938 and -4.1893938.Subproblem 1
x + -1.428571429 = 4.1893938 Simplifying x + -1.428571429 = 4.1893938 Reorder the terms: -1.428571429 + x = 4.1893938 Solving -1.428571429 + x = 4.1893938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = 4.1893938 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = 4.1893938 + 1.428571429 x = 4.1893938 + 1.428571429 Combine like terms: 4.1893938 + 1.428571429 = 5.617965229 x = 5.617965229 Simplifying x = 5.617965229Subproblem 2
x + -1.428571429 = -4.1893938 Simplifying x + -1.428571429 = -4.1893938 Reorder the terms: -1.428571429 + x = -4.1893938 Solving -1.428571429 + x = -4.1893938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = -4.1893938 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = -4.1893938 + 1.428571429 x = -4.1893938 + 1.428571429 Combine like terms: -4.1893938 + 1.428571429 = -2.760822371 x = -2.760822371 Simplifying x = -2.760822371Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.617965229, -2.760822371}
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