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Simplifying -7x2 + -2x = -7 Reorder the terms: -2x + -7x2 = -7 Solving -2x + -7x2 = -7 Solving for variable 'x'. Reorder the terms: 7 + -2x + -7x2 = -7 + 7 Combine like terms: -7 + 7 = 0 7 + -2x + -7x2 = 0 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 = 0.8672954021 x = 0.8672954021 Simplifying x = 0.8672954021Subproblem 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 = -1.1530096879 x = -1.1530096879 Simplifying x = -1.1530096879Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8672954021, -1.1530096879}
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