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Simplifying 7x(3 + x) + -1(x + -3) = 0 (3 * 7x + x * 7x) + -1(x + -3) = 0 (21x + 7x2) + -1(x + -3) = 0 Reorder the terms: 21x + 7x2 + -1(-3 + x) = 0 21x + 7x2 + (-3 * -1 + x * -1) = 0 21x + 7x2 + (3 + -1x) = 0 Reorder the terms: 3 + 21x + -1x + 7x2 = 0 Combine like terms: 21x + -1x = 20x 3 + 20x + 7x2 = 0 Solving 3 + 20x + 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'. 0.4285714286 + 2.857142857x + x2 = 0 Move the constant term to the right: Add '-0.4285714286' to each side of the equation. 0.4285714286 + 2.857142857x + -0.4285714286 + x2 = 0 + -0.4285714286 Reorder the terms: 0.4285714286 + -0.4285714286 + 2.857142857x + x2 = 0 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + 2.857142857x + x2 = 0 + -0.4285714286 2.857142857x + x2 = 0 + -0.4285714286 Combine like terms: 0 + -0.4285714286 = -0.4285714286 2.857142857x + x2 = -0.4285714286 The x term is 2.857142857x. Take half its coefficient (1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. 2.857142857x + 2.040816328 + x2 = -0.4285714286 + 2.040816328 Reorder the terms: 2.040816328 + 2.857142857x + x2 = -0.4285714286 + 2.040816328 Combine like terms: -0.4285714286 + 2.040816328 = 1.6122448994 2.040816328 + 2.857142857x + x2 = 1.6122448994 Factor a perfect square on the left side: (x + 1.428571429)(x + 1.428571429) = 1.6122448994 Calculate the square root of the right side: 1.26974206 Break this problem into two subproblems by setting (x + 1.428571429) equal to 1.26974206 and -1.26974206.Subproblem 1
x + 1.428571429 = 1.26974206 Simplifying x + 1.428571429 = 1.26974206 Reorder the terms: 1.428571429 + x = 1.26974206 Solving 1.428571429 + x = 1.26974206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.428571429' to each side of the equation. 1.428571429 + -1.428571429 + x = 1.26974206 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + x = 1.26974206 + -1.428571429 x = 1.26974206 + -1.428571429 Combine like terms: 1.26974206 + -1.428571429 = -0.158829369 x = -0.158829369 Simplifying x = -0.158829369Subproblem 2
x + 1.428571429 = -1.26974206 Simplifying x + 1.428571429 = -1.26974206 Reorder the terms: 1.428571429 + x = -1.26974206 Solving 1.428571429 + x = -1.26974206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.428571429' to each side of the equation. 1.428571429 + -1.428571429 + x = -1.26974206 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + x = -1.26974206 + -1.428571429 x = -1.26974206 + -1.428571429 Combine like terms: -1.26974206 + -1.428571429 = -2.698313489 x = -2.698313489 Simplifying x = -2.698313489Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.158829369, -2.698313489}
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