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Simplifying 7x2 + -23x + 13 = 0 Reorder the terms: 13 + -23x + 7x2 = 0 Solving 13 + -23x + 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 + -3.285714286x + x2 = 0 Move the constant term to the right: Add '-1.857142857' to each side of the equation. 1.857142857 + -3.285714286x + -1.857142857 + x2 = 0 + -1.857142857 Reorder the terms: 1.857142857 + -1.857142857 + -3.285714286x + x2 = 0 + -1.857142857 Combine like terms: 1.857142857 + -1.857142857 = 0.000000000 0.000000000 + -3.285714286x + x2 = 0 + -1.857142857 -3.285714286x + x2 = 0 + -1.857142857 Combine like terms: 0 + -1.857142857 = -1.857142857 -3.285714286x + x2 = -1.857142857 The x term is -3.285714286x. Take half its coefficient (-1.642857143). Square it (2.698979592) and add it to both sides. Add '2.698979592' to each side of the equation. -3.285714286x + 2.698979592 + x2 = -1.857142857 + 2.698979592 Reorder the terms: 2.698979592 + -3.285714286x + x2 = -1.857142857 + 2.698979592 Combine like terms: -1.857142857 + 2.698979592 = 0.841836735 2.698979592 + -3.285714286x + x2 = 0.841836735 Factor a perfect square on the left side: (x + -1.642857143)(x + -1.642857143) = 0.841836735 Calculate the square root of the right side: 0.917516613 Break this problem into two subproblems by setting (x + -1.642857143) equal to 0.917516613 and -0.917516613.Subproblem 1
x + -1.642857143 = 0.917516613 Simplifying x + -1.642857143 = 0.917516613 Reorder the terms: -1.642857143 + x = 0.917516613 Solving -1.642857143 + x = 0.917516613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.642857143' to each side of the equation. -1.642857143 + 1.642857143 + x = 0.917516613 + 1.642857143 Combine like terms: -1.642857143 + 1.642857143 = 0.000000000 0.000000000 + x = 0.917516613 + 1.642857143 x = 0.917516613 + 1.642857143 Combine like terms: 0.917516613 + 1.642857143 = 2.560373756 x = 2.560373756 Simplifying x = 2.560373756Subproblem 2
x + -1.642857143 = -0.917516613 Simplifying x + -1.642857143 = -0.917516613 Reorder the terms: -1.642857143 + x = -0.917516613 Solving -1.642857143 + x = -0.917516613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.642857143' to each side of the equation. -1.642857143 + 1.642857143 + x = -0.917516613 + 1.642857143 Combine like terms: -1.642857143 + 1.642857143 = 0.000000000 0.000000000 + x = -0.917516613 + 1.642857143 x = -0.917516613 + 1.642857143 Combine like terms: -0.917516613 + 1.642857143 = 0.72534053 x = 0.72534053 Simplifying x = 0.72534053Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.560373756, 0.72534053}
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