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Simplifying 7x2 + -1x + -4 = 0 Reorder the terms: -4 + -1x + 7x2 = 0 Solving -4 + -1x + 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'. -0.5714285714 + -0.1428571429x + x2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + -0.1428571429x + 0.5714285714 + x2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + -0.1428571429x + x2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + -0.1428571429x + x2 = 0 + 0.5714285714 -0.1428571429x + x2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 -0.1428571429x + x2 = 0.5714285714 The x term is -0.1428571429x. Take half its coefficient (-0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. -0.1428571429x + 0.005102040819 + x2 = 0.5714285714 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429x + x2 = 0.5714285714 + 0.005102040819 Combine like terms: 0.5714285714 + 0.005102040819 = 0.576530612219 0.005102040819 + -0.1428571429x + x2 = 0.576530612219 Factor a perfect square on the left side: (x + -0.07142857145)(x + -0.07142857145) = 0.576530612219 Calculate the square root of the right side: 0.759296129 Break this problem into two subproblems by setting (x + -0.07142857145) equal to 0.759296129 and -0.759296129.Subproblem 1
x + -0.07142857145 = 0.759296129 Simplifying x + -0.07142857145 = 0.759296129 Reorder the terms: -0.07142857145 + x = 0.759296129 Solving -0.07142857145 + x = 0.759296129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + x = 0.759296129 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = 0.759296129 + 0.07142857145 x = 0.759296129 + 0.07142857145 Combine like terms: 0.759296129 + 0.07142857145 = 0.83072470045 x = 0.83072470045 Simplifying x = 0.83072470045Subproblem 2
x + -0.07142857145 = -0.759296129 Simplifying x + -0.07142857145 = -0.759296129 Reorder the terms: -0.07142857145 + x = -0.759296129 Solving -0.07142857145 + x = -0.759296129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + x = -0.759296129 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = -0.759296129 + 0.07142857145 x = -0.759296129 + 0.07142857145 Combine like terms: -0.759296129 + 0.07142857145 = -0.68786755755 x = -0.68786755755 Simplifying x = -0.68786755755Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.83072470045, -0.68786755755}
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