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Simplifying -9(5 + -3x) + 7x(x + 4) = 0 (5 * -9 + -3x * -9) + 7x(x + 4) = 0 (-45 + 27x) + 7x(x + 4) = 0 Reorder the terms: -45 + 27x + 7x(4 + x) = 0 -45 + 27x + (4 * 7x + x * 7x) = 0 -45 + 27x + (28x + 7x2) = 0 Combine like terms: 27x + 28x = 55x -45 + 55x + 7x2 = 0 Solving -45 + 55x + 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'. -6.428571429 + 7.857142857x + x2 = 0 Move the constant term to the right: Add '6.428571429' to each side of the equation. -6.428571429 + 7.857142857x + 6.428571429 + x2 = 0 + 6.428571429 Reorder the terms: -6.428571429 + 6.428571429 + 7.857142857x + x2 = 0 + 6.428571429 Combine like terms: -6.428571429 + 6.428571429 = 0.000000000 0.000000000 + 7.857142857x + x2 = 0 + 6.428571429 7.857142857x + x2 = 0 + 6.428571429 Combine like terms: 0 + 6.428571429 = 6.428571429 7.857142857x + x2 = 6.428571429 The x term is 7.857142857x. Take half its coefficient (3.928571429). Square it (15.43367347) and add it to both sides. Add '15.43367347' to each side of the equation. 7.857142857x + 15.43367347 + x2 = 6.428571429 + 15.43367347 Reorder the terms: 15.43367347 + 7.857142857x + x2 = 6.428571429 + 15.43367347 Combine like terms: 6.428571429 + 15.43367347 = 21.862244899 15.43367347 + 7.857142857x + x2 = 21.862244899 Factor a perfect square on the left side: (x + 3.928571429)(x + 3.928571429) = 21.862244899 Calculate the square root of the right side: 4.675707957 Break this problem into two subproblems by setting (x + 3.928571429) equal to 4.675707957 and -4.675707957.Subproblem 1
x + 3.928571429 = 4.675707957 Simplifying x + 3.928571429 = 4.675707957 Reorder the terms: 3.928571429 + x = 4.675707957 Solving 3.928571429 + x = 4.675707957 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.928571429' to each side of the equation. 3.928571429 + -3.928571429 + x = 4.675707957 + -3.928571429 Combine like terms: 3.928571429 + -3.928571429 = 0.000000000 0.000000000 + x = 4.675707957 + -3.928571429 x = 4.675707957 + -3.928571429 Combine like terms: 4.675707957 + -3.928571429 = 0.747136528 x = 0.747136528 Simplifying x = 0.747136528Subproblem 2
x + 3.928571429 = -4.675707957 Simplifying x + 3.928571429 = -4.675707957 Reorder the terms: 3.928571429 + x = -4.675707957 Solving 3.928571429 + x = -4.675707957 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.928571429' to each side of the equation. 3.928571429 + -3.928571429 + x = -4.675707957 + -3.928571429 Combine like terms: 3.928571429 + -3.928571429 = 0.000000000 0.000000000 + x = -4.675707957 + -3.928571429 x = -4.675707957 + -3.928571429 Combine like terms: -4.675707957 + -3.928571429 = -8.604279386 x = -8.604279386 Simplifying x = -8.604279386Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.747136528, -8.604279386}
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