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Simplifying (7x + 7) + -1(7x2 + 5x) = 0 Reorder the terms: (7 + 7x) + -1(7x2 + 5x) = 0 Remove parenthesis around (7 + 7x) 7 + 7x + -1(7x2 + 5x) = 0 Reorder the terms: 7 + 7x + -1(5x + 7x2) = 0 7 + 7x + (5x * -1 + 7x2 * -1) = 0 7 + 7x + (-5x + -7x2) = 0 Combine like terms: 7x + -5x = 2x 7 + 2x + -7x2 = 0 Solving 7 + 2x + -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 + -0.2857142857x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.2857142857x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -0.2857142857x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.2857142857x + x2 = 0 + 1 -0.2857142857x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.2857142857x + x2 = 1 The x term is -0.2857142857x. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857x + 0.02040816328 + x2 = 1 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857x + x2 = 1 + 0.02040816328 Combine like terms: 1 + 0.02040816328 = 1.02040816328 0.02040816328 + -0.2857142857x + x2 = 1.02040816328 Factor a perfect square on the left side: (x + -0.1428571429)(x + -0.1428571429) = 1.02040816328 Calculate the square root of the right side: 1.010152545 Break this problem into two subproblems by setting (x + -0.1428571429) equal to 1.010152545 and -1.010152545.Subproblem 1
x + -0.1428571429 = 1.010152545 Simplifying x + -0.1428571429 = 1.010152545 Reorder the terms: -0.1428571429 + x = 1.010152545 Solving -0.1428571429 + x = 1.010152545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = 1.010152545 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 1.010152545 + 0.1428571429 x = 1.010152545 + 0.1428571429 Combine like terms: 1.010152545 + 0.1428571429 = 1.1530096879 x = 1.1530096879 Simplifying x = 1.1530096879Subproblem 2
x + -0.1428571429 = -1.010152545 Simplifying x + -0.1428571429 = -1.010152545 Reorder the terms: -0.1428571429 + x = -1.010152545 Solving -0.1428571429 + x = -1.010152545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = -1.010152545 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -1.010152545 + 0.1428571429 x = -1.010152545 + 0.1428571429 Combine like terms: -1.010152545 + 0.1428571429 = -0.8672954021 x = -0.8672954021 Simplifying x = -0.8672954021Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1530096879, -0.8672954021}
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