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Simplifying 4x2 + 14x = 4 Reorder the terms: 14x + 4x2 = 4 Solving 14x + 4x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + 14x + 4x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 14x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 7x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + 7x + 2x2)' equal to zero and attempt to solve: Simplifying -2 + 7x + 2x2 = 0 Solving -2 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1 + 3.5x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 3.5x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 3.5x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 3.5x + x2 = 0 + 1 3.5x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 3.5x + x2 = 1 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 = 1 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 1 + 3.0625 Combine like terms: 1 + 3.0625 = 4.0625 3.0625 + 3.5x + x2 = 4.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (x + 1.75) equal to 2.015564437 and -2.015564437.Subproblem 1
x + 1.75 = 2.015564437 Simplifying x + 1.75 = 2.015564437 Reorder the terms: 1.75 + x = 2.015564437 Solving 1.75 + x = 2.015564437 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 = 2.015564437 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 2.015564437 + -1.75 x = 2.015564437 + -1.75 Combine like terms: 2.015564437 + -1.75 = 0.265564437 x = 0.265564437 Simplifying x = 0.265564437Subproblem 2
x + 1.75 = -2.015564437 Simplifying x + 1.75 = -2.015564437 Reorder the terms: 1.75 + x = -2.015564437 Solving 1.75 + x = -2.015564437 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 = -2.015564437 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -2.015564437 + -1.75 x = -2.015564437 + -1.75 Combine like terms: -2.015564437 + -1.75 = -3.765564437 x = -3.765564437 Simplifying x = -3.765564437Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.265564437, -3.765564437}Solution
x = {0.265564437, -3.765564437}
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