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Simplifying 4x2 + -13x + 6 = 0 Reorder the terms: 6 + -13x + 4x2 = 0 Solving 6 + -13x + 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'. 1.5 + -3.25x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -3.25x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -3.25x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -3.25x + x2 = 0 + -1.5 -3.25x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -3.25x + x2 = -1.5 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 = -1.5 + 2.640625 Reorder the terms: 2.640625 + -3.25x + x2 = -1.5 + 2.640625 Combine like terms: -1.5 + 2.640625 = 1.140625 2.640625 + -3.25x + x2 = 1.140625 Factor a perfect square on the left side: (x + -1.625)(x + -1.625) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (x + -1.625) equal to 1.068000468 and -1.068000468.Subproblem 1
x + -1.625 = 1.068000468 Simplifying x + -1.625 = 1.068000468 Reorder the terms: -1.625 + x = 1.068000468 Solving -1.625 + x = 1.068000468 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 = 1.068000468 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = 1.068000468 + 1.625 x = 1.068000468 + 1.625 Combine like terms: 1.068000468 + 1.625 = 2.693000468 x = 2.693000468 Simplifying x = 2.693000468Subproblem 2
x + -1.625 = -1.068000468 Simplifying x + -1.625 = -1.068000468 Reorder the terms: -1.625 + x = -1.068000468 Solving -1.625 + x = -1.068000468 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 = -1.068000468 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = -1.068000468 + 1.625 x = -1.068000468 + 1.625 Combine like terms: -1.068000468 + 1.625 = 0.556999532 x = 0.556999532 Simplifying x = 0.556999532Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.693000468, 0.556999532}
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