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Simplifying 2x2 + 14x = 1 Reorder the terms: 14x + 2x2 = 1 Solving 14x + 2x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + 14x + 2x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 14x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + 7x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 7x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 7x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 7x + x2 = 0 + 0.5 7x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 7x + x2 = 0.5 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 = 0.5 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 0.5 + 12.25 Combine like terms: 0.5 + 12.25 = 12.75 12.25 + 7x + x2 = 12.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 12.75 Calculate the square root of the right side: 3.570714214 Break this problem into two subproblems by setting (x + 3.5) equal to 3.570714214 and -3.570714214.Subproblem 1
x + 3.5 = 3.570714214 Simplifying x + 3.5 = 3.570714214 Reorder the terms: 3.5 + x = 3.570714214 Solving 3.5 + x = 3.570714214 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 = 3.570714214 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.570714214 + -3.5 x = 3.570714214 + -3.5 Combine like terms: 3.570714214 + -3.5 = 0.070714214 x = 0.070714214 Simplifying x = 0.070714214Subproblem 2
x + 3.5 = -3.570714214 Simplifying x + 3.5 = -3.570714214 Reorder the terms: 3.5 + x = -3.570714214 Solving 3.5 + x = -3.570714214 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 = -3.570714214 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.570714214 + -3.5 x = -3.570714214 + -3.5 Combine like terms: -3.570714214 + -3.5 = -7.070714214 x = -7.070714214 Simplifying x = -7.070714214Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.070714214, -7.070714214}
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