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Simplifying 4.9x2 + -14.48x + 6.9 = 0 Reorder the terms: 6.9 + -14.48x + 4.9x2 = 0 Solving 6.9 + -14.48x + 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'. 1.408163265 + -2.955102041x + x2 = 0 Move the constant term to the right: Add '-1.408163265' to each side of the equation. 1.408163265 + -2.955102041x + -1.408163265 + x2 = 0 + -1.408163265 Reorder the terms: 1.408163265 + -1.408163265 + -2.955102041x + x2 = 0 + -1.408163265 Combine like terms: 1.408163265 + -1.408163265 = 0.000000000 0.000000000 + -2.955102041x + x2 = 0 + -1.408163265 -2.955102041x + x2 = 0 + -1.408163265 Combine like terms: 0 + -1.408163265 = -1.408163265 -2.955102041x + x2 = -1.408163265 The x term is -2.955102041x. Take half its coefficient (-1.477551021). Square it (2.183157020) and add it to both sides. Add '2.183157020' to each side of the equation. -2.955102041x + 2.183157020 + x2 = -1.408163265 + 2.183157020 Reorder the terms: 2.183157020 + -2.955102041x + x2 = -1.408163265 + 2.183157020 Combine like terms: -1.408163265 + 2.183157020 = 0.774993755 2.183157020 + -2.955102041x + x2 = 0.774993755 Factor a perfect square on the left side: (x + -1.477551021)(x + -1.477551021) = 0.774993755 Calculate the square root of the right side: 0.880337296 Break this problem into two subproblems by setting (x + -1.477551021) equal to 0.880337296 and -0.880337296.Subproblem 1
x + -1.477551021 = 0.880337296 Simplifying x + -1.477551021 = 0.880337296 Reorder the terms: -1.477551021 + x = 0.880337296 Solving -1.477551021 + x = 0.880337296 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.477551021' to each side of the equation. -1.477551021 + 1.477551021 + x = 0.880337296 + 1.477551021 Combine like terms: -1.477551021 + 1.477551021 = 0.000000000 0.000000000 + x = 0.880337296 + 1.477551021 x = 0.880337296 + 1.477551021 Combine like terms: 0.880337296 + 1.477551021 = 2.357888317 x = 2.357888317 Simplifying x = 2.357888317Subproblem 2
x + -1.477551021 = -0.880337296 Simplifying x + -1.477551021 = -0.880337296 Reorder the terms: -1.477551021 + x = -0.880337296 Solving -1.477551021 + x = -0.880337296 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.477551021' to each side of the equation. -1.477551021 + 1.477551021 + x = -0.880337296 + 1.477551021 Combine like terms: -1.477551021 + 1.477551021 = 0.000000000 0.000000000 + x = -0.880337296 + 1.477551021 x = -0.880337296 + 1.477551021 Combine like terms: -0.880337296 + 1.477551021 = 0.597213725 x = 0.597213725 Simplifying x = 0.597213725Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.357888317, 0.597213725}
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