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Simplifying 4x + 5 = x(x + -2) Reorder the terms: 5 + 4x = x(x + -2) Reorder the terms: 5 + 4x = x(-2 + x) 5 + 4x = (-2 * x + x * x) 5 + 4x = (-2x + x2) Solving 5 + 4x = -2x + x2 Solving for variable 'x'. Combine like terms: 4x + 2x = 6x 5 + 6x + -1x2 = -2x + x2 + 2x + -1x2 Reorder the terms: 5 + 6x + -1x2 = -2x + 2x + x2 + -1x2 Combine like terms: -2x + 2x = 0 5 + 6x + -1x2 = 0 + x2 + -1x2 5 + 6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 5 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + -6x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -6x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -6x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -6x + x2 = 0 + 5 -6x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -6x + x2 = 5 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 5 + 9 Reorder the terms: 9 + -6x + x2 = 5 + 9 Combine like terms: 5 + 9 = 14 9 + -6x + x2 = 14 Factor a perfect square on the left side: (x + -3)(x + -3) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x + -3) equal to 3.741657387 and -3.741657387.Subproblem 1
x + -3 = 3.741657387 Simplifying x + -3 = 3.741657387 Reorder the terms: -3 + x = 3.741657387 Solving -3 + x = 3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.741657387 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.741657387 + 3 x = 3.741657387 + 3 Combine like terms: 3.741657387 + 3 = 6.741657387 x = 6.741657387 Simplifying x = 6.741657387Subproblem 2
x + -3 = -3.741657387 Simplifying x + -3 = -3.741657387 Reorder the terms: -3 + x = -3.741657387 Solving -3 + x = -3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.741657387 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.741657387 + 3 x = -3.741657387 + 3 Combine like terms: -3.741657387 + 3 = -0.741657387 x = -0.741657387 Simplifying x = -0.741657387Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.741657387, -0.741657387}
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