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Simplifying 15x + 6x2 + -21 + x2 = 0 Reorder the terms: -21 + 15x + 6x2 + x2 = 0 Combine like terms: 6x2 + x2 = 7x2 -21 + 15x + 7x2 = 0 Solving -21 + 15x + 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'. -3 + 2.142857143x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 2.142857143x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 2.142857143x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2.142857143x + x2 = 0 + 3 2.142857143x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 2.142857143x + x2 = 3 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 = 3 + 1.147959185 Reorder the terms: 1.147959185 + 2.142857143x + x2 = 3 + 1.147959185 Combine like terms: 3 + 1.147959185 = 4.147959185 1.147959185 + 2.142857143x + x2 = 4.147959185 Factor a perfect square on the left side: (x + 1.071428572)(x + 1.071428572) = 4.147959185 Calculate the square root of the right side: 2.036653919 Break this problem into two subproblems by setting (x + 1.071428572) equal to 2.036653919 and -2.036653919.Subproblem 1
x + 1.071428572 = 2.036653919 Simplifying x + 1.071428572 = 2.036653919 Reorder the terms: 1.071428572 + x = 2.036653919 Solving 1.071428572 + x = 2.036653919 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 = 2.036653919 + -1.071428572 Combine like terms: 1.071428572 + -1.071428572 = 0.000000000 0.000000000 + x = 2.036653919 + -1.071428572 x = 2.036653919 + -1.071428572 Combine like terms: 2.036653919 + -1.071428572 = 0.965225347 x = 0.965225347 Simplifying x = 0.965225347Subproblem 2
x + 1.071428572 = -2.036653919 Simplifying x + 1.071428572 = -2.036653919 Reorder the terms: 1.071428572 + x = -2.036653919 Solving 1.071428572 + x = -2.036653919 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 = -2.036653919 + -1.071428572 Combine like terms: 1.071428572 + -1.071428572 = 0.000000000 0.000000000 + x = -2.036653919 + -1.071428572 x = -2.036653919 + -1.071428572 Combine like terms: -2.036653919 + -1.071428572 = -3.108082491 x = -3.108082491 Simplifying x = -3.108082491Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.965225347, -3.108082491}
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