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Simplifying 13 = 3 + 5(x + -2 + -2) * x + 5 Reorder the terms: 13 = 3 + 5(-2 + -2 + x) * x + 5 Combine like terms: -2 + -2 = -4 13 = 3 + 5(-4 + x) * x + 5 Reorder the terms for easier multiplication: 13 = 3 + 5x(-4 + x) + 5 13 = 3 + (-4 * 5x + x * 5x) + 5 13 = 3 + (-20x + 5x2) + 5 Reorder the terms: 13 = 3 + 5 + -20x + 5x2 Combine like terms: 3 + 5 = 8 13 = 8 + -20x + 5x2 Solving 13 = 8 + -20x + 5x2 Solving for variable 'x'. Combine like terms: 13 + -8 = 5 5 + 20x + -5x2 = 8 + -20x + 5x2 + -8 + 20x + -5x2 Reorder the terms: 5 + 20x + -5x2 = 8 + -8 + -20x + 20x + 5x2 + -5x2 Combine like terms: 8 + -8 = 0 5 + 20x + -5x2 = 0 + -20x + 20x + 5x2 + -5x2 5 + 20x + -5x2 = -20x + 20x + 5x2 + -5x2 Combine like terms: -20x + 20x = 0 5 + 20x + -5x2 = 0 + 5x2 + -5x2 5 + 20x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 5 + 20x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(1 + 4x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + 4x + -1x2)' equal to zero and attempt to solve: Simplifying 1 + 4x + -1x2 = 0 Solving 1 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + -4x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -4x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -4x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4x + x2 = 0 + 1 -4x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -4x + x2 = 1 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 1 + 4 Reorder the terms: 4 + -4x + x2 = 1 + 4 Combine like terms: 1 + 4 = 5 4 + -4x + x2 = 5 Factor a perfect square on the left side: (x + -2)(x + -2) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + -2) equal to 2.236067978 and -2.236067978.Subproblem 1
x + -2 = 2.236067978 Simplifying x + -2 = 2.236067978 Reorder the terms: -2 + x = 2.236067978 Solving -2 + x = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.236067978 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.236067978 + 2 x = 2.236067978 + 2 Combine like terms: 2.236067978 + 2 = 4.236067978 x = 4.236067978 Simplifying x = 4.236067978Subproblem 2
x + -2 = -2.236067978 Simplifying x + -2 = -2.236067978 Reorder the terms: -2 + x = -2.236067978 Solving -2 + x = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.236067978 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.236067978 + 2 x = -2.236067978 + 2 Combine like terms: -2.236067978 + 2 = -0.236067978 x = -0.236067978 Simplifying x = -0.236067978Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.236067978, -0.236067978}Solution
x = {4.236067978, -0.236067978}
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