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Simplifying 4x2 = 13x + -2 Reorder the terms: 4x2 = -2 + 13x Solving 4x2 = -2 + 13x Solving for variable 'x'. Reorder the terms: 2 + -13x + 4x2 = -2 + 13x + 2 + -13x Reorder the terms: 2 + -13x + 4x2 = -2 + 2 + 13x + -13x Combine like terms: -2 + 2 = 0 2 + -13x + 4x2 = 0 + 13x + -13x 2 + -13x + 4x2 = 13x + -13x Combine like terms: 13x + -13x = 0 2 + -13x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.5 + -3.25x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -3.25x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -3.25x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -3.25x + x2 = 0 + -0.5 -3.25x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -3.25x + x2 = -0.5 The x term is -3.25x. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25x + 2.640625 + x2 = -0.5 + 2.640625 Reorder the terms: 2.640625 + -3.25x + x2 = -0.5 + 2.640625 Combine like terms: -0.5 + 2.640625 = 2.140625 2.640625 + -3.25x + x2 = 2.140625 Factor a perfect square on the left side: (x + -1.625)(x + -1.625) = 2.140625 Calculate the square root of the right side: 1.463087489 Break this problem into two subproblems by setting (x + -1.625) equal to 1.463087489 and -1.463087489.Subproblem 1
x + -1.625 = 1.463087489 Simplifying x + -1.625 = 1.463087489 Reorder the terms: -1.625 + x = 1.463087489 Solving -1.625 + x = 1.463087489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = 1.463087489 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = 1.463087489 + 1.625 x = 1.463087489 + 1.625 Combine like terms: 1.463087489 + 1.625 = 3.088087489 x = 3.088087489 Simplifying x = 3.088087489Subproblem 2
x + -1.625 = -1.463087489 Simplifying x + -1.625 = -1.463087489 Reorder the terms: -1.625 + x = -1.463087489 Solving -1.625 + x = -1.463087489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = -1.463087489 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = -1.463087489 + 1.625 x = -1.463087489 + 1.625 Combine like terms: -1.463087489 + 1.625 = 0.161912511 x = 0.161912511 Simplifying x = 0.161912511Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.088087489, 0.161912511}
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