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Simplifying 4x(x) + -5 = -14x Multiply x * x 4x2 + -5 = -14x Reorder the terms: -5 + 4x2 = -14x Solving -5 + 4x2 = -14x Solving for variable 'x'. Reorder the terms: -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 = 0.326655966 x = 0.326655966 Simplifying x = 0.326655966Subproblem 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 = -3.826655966 x = -3.826655966 Simplifying x = -3.826655966Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.326655966, -3.826655966}
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