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Simplifying 7x2 + -15x = 1 Reorder the terms: -15x + 7x2 = 1 Solving -15x + 7x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -15x + 7x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -15x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.1428571429 + -2.142857143x + x2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + -2.142857143x + 0.1428571429 + x2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + -2.142857143x + x2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + -2.142857143x + x2 = 0 + 0.1428571429 -2.142857143x + x2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 -2.142857143x + x2 = 0.1428571429 The x term is -2.142857143x. Take half its coefficient (-1.071428572). Square it (1.147959185) and add it to both sides. Add '1.147959185' to each side of the equation. -2.142857143x + 1.147959185 + x2 = 0.1428571429 + 1.147959185 Reorder the terms: 1.147959185 + -2.142857143x + x2 = 0.1428571429 + 1.147959185 Combine like terms: 0.1428571429 + 1.147959185 = 1.2908163279 1.147959185 + -2.142857143x + x2 = 1.2908163279 Factor a perfect square on the left side: (x + -1.071428572)(x + -1.071428572) = 1.2908163279 Calculate the square root of the right side: 1.136140981 Break this problem into two subproblems by setting (x + -1.071428572) equal to 1.136140981 and -1.136140981.Subproblem 1
x + -1.071428572 = 1.136140981 Simplifying x + -1.071428572 = 1.136140981 Reorder the terms: -1.071428572 + x = 1.136140981 Solving -1.071428572 + x = 1.136140981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.071428572' to each side of the equation. -1.071428572 + 1.071428572 + x = 1.136140981 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + x = 1.136140981 + 1.071428572 x = 1.136140981 + 1.071428572 Combine like terms: 1.136140981 + 1.071428572 = 2.207569553 x = 2.207569553 Simplifying x = 2.207569553Subproblem 2
x + -1.071428572 = -1.136140981 Simplifying x + -1.071428572 = -1.136140981 Reorder the terms: -1.071428572 + x = -1.136140981 Solving -1.071428572 + x = -1.136140981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.071428572' to each side of the equation. -1.071428572 + 1.071428572 + x = -1.136140981 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + x = -1.136140981 + 1.071428572 x = -1.136140981 + 1.071428572 Combine like terms: -1.136140981 + 1.071428572 = -0.064712409 x = -0.064712409 Simplifying x = -0.064712409Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.207569553, -0.064712409}
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