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Simplifying 4x2 + 14x + 8 = 0 Reorder the terms: 8 + 14x + 4x2 = 0 Solving 8 + 14x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 7x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + 7x + 2x2)' equal to zero and attempt to solve: Simplifying 4 + 7x + 2x2 = 0 Solving 4 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2 + 3.5x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 3.5x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 3.5x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3.5x + x2 = 0 + -2 3.5x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 3.5x + x2 = -2 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 = -2 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = -2 + 3.0625 Combine like terms: -2 + 3.0625 = 1.0625 3.0625 + 3.5x + x2 = 1.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (x + 1.75) equal to 1.030776406 and -1.030776406.Subproblem 1
x + 1.75 = 1.030776406 Simplifying x + 1.75 = 1.030776406 Reorder the terms: 1.75 + x = 1.030776406 Solving 1.75 + x = 1.030776406 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 = 1.030776406 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 1.030776406 + -1.75 x = 1.030776406 + -1.75 Combine like terms: 1.030776406 + -1.75 = -0.719223594 x = -0.719223594 Simplifying x = -0.719223594Subproblem 2
x + 1.75 = -1.030776406 Simplifying x + 1.75 = -1.030776406 Reorder the terms: 1.75 + x = -1.030776406 Solving 1.75 + x = -1.030776406 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 = -1.030776406 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -1.030776406 + -1.75 x = -1.030776406 + -1.75 Combine like terms: -1.030776406 + -1.75 = -2.780776406 x = -2.780776406 Simplifying x = -2.780776406Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.719223594, -2.780776406}Solution
x = {-0.719223594, -2.780776406}
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