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Simplifying 7x2 + 119x + 140 = 0 Reorder the terms: 140 + 119x + 7x2 = 0 Solving 140 + 119x + 7x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7'. 7(20 + 17x + x2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(20 + 17x + x2)' equal to zero and attempt to solve: Simplifying 20 + 17x + x2 = 0 Solving 20 + 17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + 17x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + 17x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 17x + x2 = 0 + -20 17x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 17x + x2 = -20 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = -20 + 72.25 Reorder the terms: 72.25 + 17x + x2 = -20 + 72.25 Combine like terms: -20 + 72.25 = 52.25 72.25 + 17x + x2 = 52.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (x + 8.5) equal to 7.228416147 and -7.228416147.Subproblem 1
x + 8.5 = 7.228416147 Simplifying x + 8.5 = 7.228416147 Reorder the terms: 8.5 + x = 7.228416147 Solving 8.5 + x = 7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 7.228416147 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 7.228416147 + -8.5 x = 7.228416147 + -8.5 Combine like terms: 7.228416147 + -8.5 = -1.271583853 x = -1.271583853 Simplifying x = -1.271583853Subproblem 2
x + 8.5 = -7.228416147 Simplifying x + 8.5 = -7.228416147 Reorder the terms: 8.5 + x = -7.228416147 Solving 8.5 + x = -7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -7.228416147 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -7.228416147 + -8.5 x = -7.228416147 + -8.5 Combine like terms: -7.228416147 + -8.5 = -15.728416147 x = -15.728416147 Simplifying x = -15.728416147Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.271583853, -15.728416147}Solution
x = {-1.271583853, -15.728416147}
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