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Simplifying 14x2 + 28x + -240 = 0 Reorder the terms: -240 + 28x + 14x2 = 0 Solving -240 + 28x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-120 + 14x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-120 + 14x + 7x2)' equal to zero and attempt to solve: Simplifying -120 + 14x + 7x2 = 0 Solving -120 + 14x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -17.14285714 + 2x + x2 = 0 Move the constant term to the right: Add '17.14285714' to each side of the equation. -17.14285714 + 2x + 17.14285714 + x2 = 0 + 17.14285714 Reorder the terms: -17.14285714 + 17.14285714 + 2x + x2 = 0 + 17.14285714 Combine like terms: -17.14285714 + 17.14285714 = 0.00000000 0.00000000 + 2x + x2 = 0 + 17.14285714 2x + x2 = 0 + 17.14285714 Combine like terms: 0 + 17.14285714 = 17.14285714 2x + x2 = 17.14285714 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 = 17.14285714 + 1 Reorder the terms: 1 + 2x + x2 = 17.14285714 + 1 Combine like terms: 17.14285714 + 1 = 18.14285714 1 + 2x + x2 = 18.14285714 Factor a perfect square on the left side: (x + 1)(x + 1) = 18.14285714 Calculate the square root of the right side: 4.25944329 Break this problem into two subproblems by setting (x + 1) equal to 4.25944329 and -4.25944329.Subproblem 1
x + 1 = 4.25944329 Simplifying x + 1 = 4.25944329 Reorder the terms: 1 + x = 4.25944329 Solving 1 + x = 4.25944329 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 = 4.25944329 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.25944329 + -1 x = 4.25944329 + -1 Combine like terms: 4.25944329 + -1 = 3.25944329 x = 3.25944329 Simplifying x = 3.25944329Subproblem 2
x + 1 = -4.25944329 Simplifying x + 1 = -4.25944329 Reorder the terms: 1 + x = -4.25944329 Solving 1 + x = -4.25944329 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 = -4.25944329 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.25944329 + -1 x = -4.25944329 + -1 Combine like terms: -4.25944329 + -1 = -5.25944329 x = -5.25944329 Simplifying x = -5.25944329Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.25944329, -5.25944329}Solution
x = {3.25944329, -5.25944329}
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