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Simplifying 4x2 + 14x + -13 = 0 Reorder the terms: -13 + 14x + 4x2 = 0 Solving -13 + 14x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.25 + 3.5x + x2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + 3.5x + 3.25 + x2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + 3.5x + x2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + 3.5x + x2 = 0 + 3.25 3.5x + x2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 3.5x + x2 = 3.25 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 = 3.25 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 3.25 + 3.0625 Combine like terms: 3.25 + 3.0625 = 6.3125 3.0625 + 3.5x + x2 = 6.3125 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 6.3125 Calculate the square root of the right side: 2.512468905 Break this problem into two subproblems by setting (x + 1.75) equal to 2.512468905 and -2.512468905.Subproblem 1
x + 1.75 = 2.512468905 Simplifying x + 1.75 = 2.512468905 Reorder the terms: 1.75 + x = 2.512468905 Solving 1.75 + x = 2.512468905 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 = 2.512468905 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 2.512468905 + -1.75 x = 2.512468905 + -1.75 Combine like terms: 2.512468905 + -1.75 = 0.762468905 x = 0.762468905 Simplifying x = 0.762468905Subproblem 2
x + 1.75 = -2.512468905 Simplifying x + 1.75 = -2.512468905 Reorder the terms: 1.75 + x = -2.512468905 Solving 1.75 + x = -2.512468905 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 = -2.512468905 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -2.512468905 + -1.75 x = -2.512468905 + -1.75 Combine like terms: -2.512468905 + -1.75 = -4.262468905 x = -4.262468905 Simplifying x = -4.262468905Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.762468905, -4.262468905}
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