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Simplifying 10x2 + 5 + -7x + -6x2 + -13x = 0 Reorder the terms: 5 + -7x + -13x + 10x2 + -6x2 = 0 Combine like terms: -7x + -13x = -20x 5 + -20x + 10x2 + -6x2 = 0 Combine like terms: 10x2 + -6x2 = 4x2 5 + -20x + 4x2 = 0 Solving 5 + -20x + 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'. 1.25 + -5x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -5x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -5x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -5x + x2 = 0 + -1.25 -5x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -5x + x2 = -1.25 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 = -1.25 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -1.25 + 6.25 Combine like terms: -1.25 + 6.25 = 5 6.25 + -5x + x2 = 5 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + -2.5) equal to 2.236067978 and -2.236067978.Subproblem 1
x + -2.5 = 2.236067978 Simplifying x + -2.5 = 2.236067978 Reorder the terms: -2.5 + x = 2.236067978 Solving -2.5 + x = 2.236067978 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 = 2.236067978 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.236067978 + 2.5 x = 2.236067978 + 2.5 Combine like terms: 2.236067978 + 2.5 = 4.736067978 x = 4.736067978 Simplifying x = 4.736067978Subproblem 2
x + -2.5 = -2.236067978 Simplifying x + -2.5 = -2.236067978 Reorder the terms: -2.5 + x = -2.236067978 Solving -2.5 + x = -2.236067978 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 = -2.236067978 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.236067978 + 2.5 x = -2.236067978 + 2.5 Combine like terms: -2.236067978 + 2.5 = 0.263932022 x = 0.263932022 Simplifying x = 0.263932022Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.736067978, 0.263932022}
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