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Simplifying 4x + 13 = x2 + -4 Reorder the terms: 13 + 4x = x2 + -4 Reorder the terms: 13 + 4x = -4 + x2 Solving 13 + 4x = -4 + x2 Solving for variable 'x'. Reorder the terms: 13 + 4 + 4x + -1x2 = -4 + x2 + 4 + -1x2 Combine like terms: 13 + 4 = 17 17 + 4x + -1x2 = -4 + x2 + 4 + -1x2 Reorder the terms: 17 + 4x + -1x2 = -4 + 4 + x2 + -1x2 Combine like terms: -4 + 4 = 0 17 + 4x + -1x2 = 0 + x2 + -1x2 17 + 4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 17 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -17 + -4x + x2 = 0 Move the constant term to the right: Add '17' to each side of the equation. -17 + -4x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + -4x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -4x + x2 = 0 + 17 -4x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 -4x + x2 = 17 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 = 17 + 4 Reorder the terms: 4 + -4x + x2 = 17 + 4 Combine like terms: 17 + 4 = 21 4 + -4x + x2 = 21 Factor a perfect square on the left side: (x + -2)(x + -2) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (x + -2) equal to 4.582575695 and -4.582575695.Subproblem 1
x + -2 = 4.582575695 Simplifying x + -2 = 4.582575695 Reorder the terms: -2 + x = 4.582575695 Solving -2 + x = 4.582575695 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 = 4.582575695 + 2 Combine like terms: -2 + 2 = 0 0 + x = 4.582575695 + 2 x = 4.582575695 + 2 Combine like terms: 4.582575695 + 2 = 6.582575695 x = 6.582575695 Simplifying x = 6.582575695Subproblem 2
x + -2 = -4.582575695 Simplifying x + -2 = -4.582575695 Reorder the terms: -2 + x = -4.582575695 Solving -2 + x = -4.582575695 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 = -4.582575695 + 2 Combine like terms: -2 + 2 = 0 0 + x = -4.582575695 + 2 x = -4.582575695 + 2 Combine like terms: -4.582575695 + 2 = -2.582575695 x = -2.582575695 Simplifying x = -2.582575695Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.582575695, -2.582575695}
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