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Simplifying -4.9x2 + 14x + 400 = 0 Reorder the terms: 400 + 14x + -4.9x2 = 0 Solving 400 + 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'. -81.63265306 + -2.857142857x + x2 = 0 Move the constant term to the right: Add '81.63265306' to each side of the equation. -81.63265306 + -2.857142857x + 81.63265306 + x2 = 0 + 81.63265306 Reorder the terms: -81.63265306 + 81.63265306 + -2.857142857x + x2 = 0 + 81.63265306 Combine like terms: -81.63265306 + 81.63265306 = 0.00000000 0.00000000 + -2.857142857x + x2 = 0 + 81.63265306 -2.857142857x + x2 = 0 + 81.63265306 Combine like terms: 0 + 81.63265306 = 81.63265306 -2.857142857x + x2 = 81.63265306 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 = 81.63265306 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857x + x2 = 81.63265306 + 2.040816328 Combine like terms: 81.63265306 + 2.040816328 = 83.673469388 2.040816328 + -2.857142857x + x2 = 83.673469388 Factor a perfect square on the left side: (x + -1.428571429)(x + -1.428571429) = 83.673469388 Calculate the square root of the right side: 9.147320339 Break this problem into two subproblems by setting (x + -1.428571429) equal to 9.147320339 and -9.147320339.Subproblem 1
x + -1.428571429 = 9.147320339 Simplifying x + -1.428571429 = 9.147320339 Reorder the terms: -1.428571429 + x = 9.147320339 Solving -1.428571429 + x = 9.147320339 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 = 9.147320339 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = 9.147320339 + 1.428571429 x = 9.147320339 + 1.428571429 Combine like terms: 9.147320339 + 1.428571429 = 10.575891768 x = 10.575891768 Simplifying x = 10.575891768Subproblem 2
x + -1.428571429 = -9.147320339 Simplifying x + -1.428571429 = -9.147320339 Reorder the terms: -1.428571429 + x = -9.147320339 Solving -1.428571429 + x = -9.147320339 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 = -9.147320339 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = -9.147320339 + 1.428571429 x = -9.147320339 + 1.428571429 Combine like terms: -9.147320339 + 1.428571429 = -7.71874891 x = -7.71874891 Simplifying x = -7.71874891Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.575891768, -7.71874891}
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