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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 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 14x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 14x + 2x2)' equal to zero and attempt to solve: Simplifying 1 + 14x + 2x2 = 0 Solving 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 = 11.75 12.25 + 7x + x2 = 11.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 11.75 Calculate the square root of the right side: 3.4278273 Break this problem into two subproblems by setting (x + 3.5) equal to 3.4278273 and -3.4278273.Subproblem 1
x + 3.5 = 3.4278273 Simplifying x + 3.5 = 3.4278273 Reorder the terms: 3.5 + x = 3.4278273 Solving 3.5 + x = 3.4278273 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 = 3.4278273 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.4278273 + -3.5 x = 3.4278273 + -3.5 Combine like terms: 3.4278273 + -3.5 = -0.0721727 x = -0.0721727 Simplifying x = -0.0721727Subproblem 2
x + 3.5 = -3.4278273 Simplifying x + 3.5 = -3.4278273 Reorder the terms: 3.5 + x = -3.4278273 Solving 3.5 + x = -3.4278273 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 = -3.4278273 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.4278273 + -3.5 x = -3.4278273 + -3.5 Combine like terms: -3.4278273 + -3.5 = -6.9278273 x = -6.9278273 Simplifying x = -6.9278273Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0721727, -6.9278273}Solution
x = {-0.0721727, -6.9278273}
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