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Simplifying -7x2 + -14x + -5 = 0 Reorder the terms: -5 + -14x + -7x2 = 0 Solving -5 + -14x + -7x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 14x + 7x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 14x + 7x2)' equal to zero and attempt to solve: Simplifying 5 + 14x + 7x2 = 0 Solving 5 + 14x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.7142857143 + 2x + x2 = 0 Move the constant term to the right: Add '-0.7142857143' to each side of the equation. 0.7142857143 + 2x + -0.7142857143 + x2 = 0 + -0.7142857143 Reorder the terms: 0.7142857143 + -0.7142857143 + 2x + x2 = 0 + -0.7142857143 Combine like terms: 0.7142857143 + -0.7142857143 = 0.0000000000 0.0000000000 + 2x + x2 = 0 + -0.7142857143 2x + x2 = 0 + -0.7142857143 Combine like terms: 0 + -0.7142857143 = -0.7142857143 2x + x2 = -0.7142857143 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -0.7142857143 + 1 Reorder the terms: 1 + 2x + x2 = -0.7142857143 + 1 Combine like terms: -0.7142857143 + 1 = 0.2857142857 1 + 2x + x2 = 0.2857142857 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.2857142857 Calculate the square root of the right side: 0.534522484 Break this problem into two subproblems by setting (x + 1) equal to 0.534522484 and -0.534522484.Subproblem 1
x + 1 = 0.534522484 Simplifying x + 1 = 0.534522484 Reorder the terms: 1 + x = 0.534522484 Solving 1 + x = 0.534522484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.534522484 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.534522484 + -1 x = 0.534522484 + -1 Combine like terms: 0.534522484 + -1 = -0.465477516 x = -0.465477516 Simplifying x = -0.465477516Subproblem 2
x + 1 = -0.534522484 Simplifying x + 1 = -0.534522484 Reorder the terms: 1 + x = -0.534522484 Solving 1 + x = -0.534522484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.534522484 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.534522484 + -1 x = -0.534522484 + -1 Combine like terms: -0.534522484 + -1 = -1.534522484 x = -1.534522484 Simplifying x = -1.534522484Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.465477516, -1.534522484}Solution
x = {-0.465477516, -1.534522484}
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