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Simplifying 2x2 + 14x = -5 Reorder the terms: 14x + 2x2 = -5 Solving 14x + 2x2 = -5 Solving for variable 'x'. Reorder the terms: 5 + 14x + 2x2 = -5 + 5 Combine like terms: -5 + 5 = 0 5 + 14x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + 7x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 7x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 7x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 7x + x2 = 0 + -2.5 7x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 7x + x2 = -2.5 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -2.5 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -2.5 + 12.25 Combine like terms: -2.5 + 12.25 = 9.75 12.25 + 7x + x2 = 9.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 9.75 Calculate the square root of the right side: 3.122498999 Break this problem into two subproblems by setting (x + 3.5) equal to 3.122498999 and -3.122498999.Subproblem 1
x + 3.5 = 3.122498999 Simplifying x + 3.5 = 3.122498999 Reorder the terms: 3.5 + x = 3.122498999 Solving 3.5 + x = 3.122498999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 3.122498999 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.122498999 + -3.5 x = 3.122498999 + -3.5 Combine like terms: 3.122498999 + -3.5 = -0.377501001 x = -0.377501001 Simplifying x = -0.377501001Subproblem 2
x + 3.5 = -3.122498999 Simplifying x + 3.5 = -3.122498999 Reorder the terms: 3.5 + x = -3.122498999 Solving 3.5 + x = -3.122498999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -3.122498999 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.122498999 + -3.5 x = -3.122498999 + -3.5 Combine like terms: -3.122498999 + -3.5 = -6.622498999 x = -6.622498999 Simplifying x = -6.622498999Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.377501001, -6.622498999}
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