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Simplifying 7x2 + 10x + -10 = 0 Reorder the terms: -10 + 10x + 7x2 = 0 Solving -10 + 10x + 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'. -1.428571429 + 1.428571429x + x2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429x + 1.428571429 + x2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + 1.428571429x + x2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + 1.428571429x + x2 = 0 + 1.428571429 1.428571429x + x2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 1.428571429x + x2 = 1.428571429 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 = 1.428571429 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429x + x2 = 1.428571429 + 0.5102040819 Combine like terms: 1.428571429 + 0.5102040819 = 1.9387755109 0.5102040819 + 1.428571429x + x2 = 1.9387755109 Factor a perfect square on the left side: (x + 0.7142857145)(x + 0.7142857145) = 1.9387755109 Calculate the square root of the right side: 1.392399192 Break this problem into two subproblems by setting (x + 0.7142857145) equal to 1.392399192 and -1.392399192.Subproblem 1
x + 0.7142857145 = 1.392399192 Simplifying x + 0.7142857145 = 1.392399192 Reorder the terms: 0.7142857145 + x = 1.392399192 Solving 0.7142857145 + x = 1.392399192 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 = 1.392399192 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = 1.392399192 + -0.7142857145 x = 1.392399192 + -0.7142857145 Combine like terms: 1.392399192 + -0.7142857145 = 0.6781134775 x = 0.6781134775 Simplifying x = 0.6781134775Subproblem 2
x + 0.7142857145 = -1.392399192 Simplifying x + 0.7142857145 = -1.392399192 Reorder the terms: 0.7142857145 + x = -1.392399192 Solving 0.7142857145 + x = -1.392399192 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 = -1.392399192 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = -1.392399192 + -0.7142857145 x = -1.392399192 + -0.7142857145 Combine like terms: -1.392399192 + -0.7142857145 = -2.1066849065 x = -2.1066849065 Simplifying x = -2.1066849065Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6781134775, -2.1066849065}
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