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Simplifying 7x2 + 10x = -1 Reorder the terms: 10x + 7x2 = -1 Solving 10x + 7x2 = -1 Solving for variable 'x'. Reorder the terms: 1 + 10x + 7x2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + 10x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.1428571429 + 1.428571429x + x2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + 1.428571429x + -0.1428571429 + x2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + 1.428571429x + x2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + 1.428571429x + x2 = 0 + -0.1428571429 1.428571429x + x2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 1.428571429x + x2 = -0.1428571429 The x term is 1.428571429x. Take half its coefficient (0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. 1.428571429x + 0.5102040819 + x2 = -0.1428571429 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429x + x2 = -0.1428571429 + 0.5102040819 Combine like terms: -0.1428571429 + 0.5102040819 = 0.367346939 0.5102040819 + 1.428571429x + x2 = 0.367346939 Factor a perfect square on the left side: (x + 0.7142857145)(x + 0.7142857145) = 0.367346939 Calculate the square root of the right side: 0.606091527 Break this problem into two subproblems by setting (x + 0.7142857145) equal to 0.606091527 and -0.606091527.Subproblem 1
x + 0.7142857145 = 0.606091527 Simplifying x + 0.7142857145 = 0.606091527 Reorder the terms: 0.7142857145 + x = 0.606091527 Solving 0.7142857145 + x = 0.606091527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + x = 0.606091527 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = 0.606091527 + -0.7142857145 x = 0.606091527 + -0.7142857145 Combine like terms: 0.606091527 + -0.7142857145 = -0.1081941875 x = -0.1081941875 Simplifying x = -0.1081941875Subproblem 2
x + 0.7142857145 = -0.606091527 Simplifying x + 0.7142857145 = -0.606091527 Reorder the terms: 0.7142857145 + x = -0.606091527 Solving 0.7142857145 + x = -0.606091527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + x = -0.606091527 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = -0.606091527 + -0.7142857145 x = -0.606091527 + -0.7142857145 Combine like terms: -0.606091527 + -0.7142857145 = -1.3203772415 x = -1.3203772415 Simplifying x = -1.3203772415Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.1081941875, -1.3203772415}
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