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Simplifying 4x2 + 14x + -2 = 0 Reorder the terms: -2 + 14x + 4x2 = 0 Solving -2 + 14x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 7x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 7x + 2x2)' equal to zero and attempt to solve: Simplifying -1 + 7x + 2x2 = 0 Solving -1 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + 3.5x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 3.5x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 3.5x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 3.5x + x2 = 0 + 0.5 3.5x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 3.5x + x2 = 0.5 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 0.5 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 0.5 + 3.0625 Combine like terms: 0.5 + 3.0625 = 3.5625 3.0625 + 3.5x + x2 = 3.5625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (x + 1.75) equal to 1.887458609 and -1.887458609.Subproblem 1
x + 1.75 = 1.887458609 Simplifying x + 1.75 = 1.887458609 Reorder the terms: 1.75 + x = 1.887458609 Solving 1.75 + x = 1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 1.887458609 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 1.887458609 + -1.75 x = 1.887458609 + -1.75 Combine like terms: 1.887458609 + -1.75 = 0.137458609 x = 0.137458609 Simplifying x = 0.137458609Subproblem 2
x + 1.75 = -1.887458609 Simplifying x + 1.75 = -1.887458609 Reorder the terms: 1.75 + x = -1.887458609 Solving 1.75 + x = -1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -1.887458609 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -1.887458609 + -1.75 x = -1.887458609 + -1.75 Combine like terms: -1.887458609 + -1.75 = -3.637458609 x = -3.637458609 Simplifying x = -3.637458609Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.137458609, -3.637458609}Solution
x = {0.137458609, -3.637458609}
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