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Simplifying 7x2 + 2x + -49 = 0 Reorder the terms: -49 + 2x + 7x2 = 0 Solving -49 + 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'. -7 + 0.2857142857x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 0.2857142857x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 0.2857142857x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 0.2857142857x + x2 = 0 + 7 0.2857142857x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 0.2857142857x + x2 = 7 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 = 7 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857x + x2 = 7 + 0.02040816328 Combine like terms: 7 + 0.02040816328 = 7.02040816328 0.02040816328 + 0.2857142857x + x2 = 7.02040816328 Factor a perfect square on the left side: (x + 0.1428571429)(x + 0.1428571429) = 7.02040816328 Calculate the square root of the right side: 2.649605284 Break this problem into two subproblems by setting (x + 0.1428571429) equal to 2.649605284 and -2.649605284.Subproblem 1
x + 0.1428571429 = 2.649605284 Simplifying x + 0.1428571429 = 2.649605284 Reorder the terms: 0.1428571429 + x = 2.649605284 Solving 0.1428571429 + x = 2.649605284 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 = 2.649605284 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = 2.649605284 + -0.1428571429 x = 2.649605284 + -0.1428571429 Combine like terms: 2.649605284 + -0.1428571429 = 2.5067481411 x = 2.5067481411 Simplifying x = 2.5067481411Subproblem 2
x + 0.1428571429 = -2.649605284 Simplifying x + 0.1428571429 = -2.649605284 Reorder the terms: 0.1428571429 + x = -2.649605284 Solving 0.1428571429 + x = -2.649605284 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 = -2.649605284 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = -2.649605284 + -0.1428571429 x = -2.649605284 + -0.1428571429 Combine like terms: -2.649605284 + -0.1428571429 = -2.7924624269 x = -2.7924624269 Simplifying x = -2.7924624269Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5067481411, -2.7924624269}
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