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Simplifying 4x2 + -13x + 27 = 7x + 8 Reorder the terms: 27 + -13x + 4x2 = 7x + 8 Reorder the terms: 27 + -13x + 4x2 = 8 + 7x Solving 27 + -13x + 4x2 = 8 + 7x Solving for variable 'x'. Reorder the terms: 27 + -8 + -13x + -7x + 4x2 = 8 + 7x + -8 + -7x Combine like terms: 27 + -8 = 19 19 + -13x + -7x + 4x2 = 8 + 7x + -8 + -7x Combine like terms: -13x + -7x = -20x 19 + -20x + 4x2 = 8 + 7x + -8 + -7x Reorder the terms: 19 + -20x + 4x2 = 8 + -8 + 7x + -7x Combine like terms: 8 + -8 = 0 19 + -20x + 4x2 = 0 + 7x + -7x 19 + -20x + 4x2 = 7x + -7x Combine like terms: 7x + -7x = 0 19 + -20x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 4.75 + -5x + x2 = 0 Move the constant term to the right: Add '-4.75' to each side of the equation. 4.75 + -5x + -4.75 + x2 = 0 + -4.75 Reorder the terms: 4.75 + -4.75 + -5x + x2 = 0 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + -5x + x2 = 0 + -4.75 -5x + x2 = 0 + -4.75 Combine like terms: 0 + -4.75 = -4.75 -5x + x2 = -4.75 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -4.75 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -4.75 + 6.25 Combine like terms: -4.75 + 6.25 = 1.5 6.25 + -5x + x2 = 1.5 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (x + -2.5) equal to 1.224744871 and -1.224744871.Subproblem 1
x + -2.5 = 1.224744871 Simplifying x + -2.5 = 1.224744871 Reorder the terms: -2.5 + x = 1.224744871 Solving -2.5 + x = 1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 1.224744871 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.224744871 + 2.5 x = 1.224744871 + 2.5 Combine like terms: 1.224744871 + 2.5 = 3.724744871 x = 3.724744871 Simplifying x = 3.724744871Subproblem 2
x + -2.5 = -1.224744871 Simplifying x + -2.5 = -1.224744871 Reorder the terms: -2.5 + x = -1.224744871 Solving -2.5 + x = -1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -1.224744871 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.224744871 + 2.5 x = -1.224744871 + 2.5 Combine like terms: -1.224744871 + 2.5 = 1.275255129 x = 1.275255129 Simplifying x = 1.275255129Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.724744871, 1.275255129}
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