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Simplifying 7x2 + 4x + -13 = 0 Reorder the terms: -13 + 4x + 7x2 = 0 Solving -13 + 4x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.857142857 + 0.5714285714x + x2 = 0 Move the constant term to the right: Add '1.857142857' to each side of the equation. -1.857142857 + 0.5714285714x + 1.857142857 + x2 = 0 + 1.857142857 Reorder the terms: -1.857142857 + 1.857142857 + 0.5714285714x + x2 = 0 + 1.857142857 Combine like terms: -1.857142857 + 1.857142857 = 0.000000000 0.000000000 + 0.5714285714x + x2 = 0 + 1.857142857 0.5714285714x + x2 = 0 + 1.857142857 Combine like terms: 0 + 1.857142857 = 1.857142857 0.5714285714x + x2 = 1.857142857 The x term is 0.5714285714x. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714x + 0.08163265305 + x2 = 1.857142857 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714x + x2 = 1.857142857 + 0.08163265305 Combine like terms: 1.857142857 + 0.08163265305 = 1.93877551005 0.08163265305 + 0.5714285714x + x2 = 1.93877551005 Factor a perfect square on the left side: (x + 0.2857142857)(x + 0.2857142857) = 1.93877551005 Calculate the square root of the right side: 1.392399192 Break this problem into two subproblems by setting (x + 0.2857142857) equal to 1.392399192 and -1.392399192.Subproblem 1
x + 0.2857142857 = 1.392399192 Simplifying x + 0.2857142857 = 1.392399192 Reorder the terms: 0.2857142857 + x = 1.392399192 Solving 0.2857142857 + x = 1.392399192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = 1.392399192 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = 1.392399192 + -0.2857142857 x = 1.392399192 + -0.2857142857 Combine like terms: 1.392399192 + -0.2857142857 = 1.1066849063 x = 1.1066849063 Simplifying x = 1.1066849063Subproblem 2
x + 0.2857142857 = -1.392399192 Simplifying x + 0.2857142857 = -1.392399192 Reorder the terms: 0.2857142857 + x = -1.392399192 Solving 0.2857142857 + x = -1.392399192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = -1.392399192 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = -1.392399192 + -0.2857142857 x = -1.392399192 + -0.2857142857 Combine like terms: -1.392399192 + -0.2857142857 = -1.6781134777 x = -1.6781134777 Simplifying x = -1.6781134777Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1066849063, -1.6781134777}
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