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Simplifying 5 + -1x(x + 3) = -1(x + 5) Reorder the terms: 5 + -1x(3 + x) = -1(x + 5) 5 + (3 * -1x + x * -1x) = -1(x + 5) 5 + (-3x + -1x2) = -1(x + 5) Reorder the terms: 5 + -3x + -1x2 = -1(5 + x) 5 + -3x + -1x2 = (5 * -1 + x * -1) 5 + -3x + -1x2 = (-5 + -1x) Solving 5 + -3x + -1x2 = -5 + -1x Solving for variable 'x'. Reorder the terms: 5 + 5 + -3x + x + -1x2 = -5 + -1x + 5 + x Combine like terms: 5 + 5 = 10 10 + -3x + x + -1x2 = -5 + -1x + 5 + x Combine like terms: -3x + x = -2x 10 + -2x + -1x2 = -5 + -1x + 5 + x Reorder the terms: 10 + -2x + -1x2 = -5 + 5 + -1x + x Combine like terms: -5 + 5 = 0 10 + -2x + -1x2 = 0 + -1x + x 10 + -2x + -1x2 = -1x + x Combine like terms: -1x + x = 0 10 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10 + 2x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 2x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 2x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 2x + x2 = 0 + 10 2x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 2x + x2 = 10 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 10 + 1 Reorder the terms: 1 + 2x + x2 = 10 + 1 Combine like terms: 10 + 1 = 11 1 + 2x + x2 = 11 Factor a perfect square on the left side: (x + 1)(x + 1) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + 1) equal to 3.31662479 and -3.31662479.Subproblem 1
x + 1 = 3.31662479 Simplifying x + 1 = 3.31662479 Reorder the terms: 1 + x = 3.31662479 Solving 1 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 3.31662479 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.31662479 + -1 x = 3.31662479 + -1 Combine like terms: 3.31662479 + -1 = 2.31662479 x = 2.31662479 Simplifying x = 2.31662479Subproblem 2
x + 1 = -3.31662479 Simplifying x + 1 = -3.31662479 Reorder the terms: 1 + x = -3.31662479 Solving 1 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -3.31662479 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.31662479 + -1 x = -3.31662479 + -1 Combine like terms: -3.31662479 + -1 = -4.31662479 x = -4.31662479 Simplifying x = -4.31662479Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.31662479, -4.31662479}
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