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Simplifying 7x2 + 100x + -4 = 0 Reorder the terms: -4 + 100x + 7x2 = 0 Solving -4 + 100x + 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 + 14.28571429x + x2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + 14.28571429x + 0.5714285714 + x2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + 14.28571429x + x2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + 14.28571429x + x2 = 0 + 0.5714285714 14.28571429x + x2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 14.28571429x + x2 = 0.5714285714 The x term is 14.28571429x. Take half its coefficient (7.142857145). Square it (51.02040819) and add it to both sides. Add '51.02040819' to each side of the equation. 14.28571429x + 51.02040819 + x2 = 0.5714285714 + 51.02040819 Reorder the terms: 51.02040819 + 14.28571429x + x2 = 0.5714285714 + 51.02040819 Combine like terms: 0.5714285714 + 51.02040819 = 51.5918367614 51.02040819 + 14.28571429x + x2 = 51.5918367614 Factor a perfect square on the left side: (x + 7.142857145)(x + 7.142857145) = 51.5918367614 Calculate the square root of the right side: 7.182745768 Break this problem into two subproblems by setting (x + 7.142857145) equal to 7.182745768 and -7.182745768.Subproblem 1
x + 7.142857145 = 7.182745768 Simplifying x + 7.142857145 = 7.182745768 Reorder the terms: 7.142857145 + x = 7.182745768 Solving 7.142857145 + x = 7.182745768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.142857145' to each side of the equation. 7.142857145 + -7.142857145 + x = 7.182745768 + -7.142857145 Combine like terms: 7.142857145 + -7.142857145 = 0.000000000 0.000000000 + x = 7.182745768 + -7.142857145 x = 7.182745768 + -7.142857145 Combine like terms: 7.182745768 + -7.142857145 = 0.039888623 x = 0.039888623 Simplifying x = 0.039888623Subproblem 2
x + 7.142857145 = -7.182745768 Simplifying x + 7.142857145 = -7.182745768 Reorder the terms: 7.142857145 + x = -7.182745768 Solving 7.142857145 + x = -7.182745768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.142857145' to each side of the equation. 7.142857145 + -7.142857145 + x = -7.182745768 + -7.142857145 Combine like terms: 7.142857145 + -7.142857145 = 0.000000000 0.000000000 + x = -7.182745768 + -7.142857145 x = -7.182745768 + -7.142857145 Combine like terms: -7.182745768 + -7.142857145 = -14.325602913 x = -14.325602913 Simplifying x = -14.325602913Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.039888623, -14.325602913}
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