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Simplifying 4x2 = 14x + 5 Reorder the terms: 4x2 = 5 + 14x Solving 4x2 = 5 + 14x Solving for variable 'x'. Reorder the terms: -5 + -14x + 4x2 = 5 + 14x + -5 + -14x Reorder the terms: -5 + -14x + 4x2 = 5 + -5 + 14x + -14x Combine like terms: 5 + -5 = 0 -5 + -14x + 4x2 = 0 + 14x + -14x -5 + -14x + 4x2 = 14x + -14x Combine like terms: 14x + -14x = 0 -5 + -14x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + -3.5x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -3.5x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -3.5x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -3.5x + x2 = 0 + 1.25 -3.5x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -3.5x + x2 = 1.25 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 = 1.25 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 1.25 + 3.0625 Combine like terms: 1.25 + 3.0625 = 4.3125 3.0625 + -3.5x + x2 = 4.3125 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 4.3125 Calculate the square root of the right side: 2.076655966 Break this problem into two subproblems by setting (x + -1.75) equal to 2.076655966 and -2.076655966.Subproblem 1
x + -1.75 = 2.076655966 Simplifying x + -1.75 = 2.076655966 Reorder the terms: -1.75 + x = 2.076655966 Solving -1.75 + x = 2.076655966 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 = 2.076655966 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 2.076655966 + 1.75 x = 2.076655966 + 1.75 Combine like terms: 2.076655966 + 1.75 = 3.826655966 x = 3.826655966 Simplifying x = 3.826655966Subproblem 2
x + -1.75 = -2.076655966 Simplifying x + -1.75 = -2.076655966 Reorder the terms: -1.75 + x = -2.076655966 Solving -1.75 + x = -2.076655966 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 = -2.076655966 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -2.076655966 + 1.75 x = -2.076655966 + 1.75 Combine like terms: -2.076655966 + 1.75 = -0.326655966 x = -0.326655966 Simplifying x = -0.326655966Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.826655966, -0.326655966}
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