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Simplifying 2x(x + 5) = x(3x + -1) + -4 Reorder the terms: 2x(5 + x) = x(3x + -1) + -4 (5 * 2x + x * 2x) = x(3x + -1) + -4 (10x + 2x2) = x(3x + -1) + -4 Reorder the terms: 10x + 2x2 = x(-1 + 3x) + -4 10x + 2x2 = (-1 * x + 3x * x) + -4 10x + 2x2 = (-1x + 3x2) + -4 Reorder the terms: 10x + 2x2 = -4 + -1x + 3x2 Solving 10x + 2x2 = -4 + -1x + 3x2 Solving for variable 'x'. Reorder the terms: 4 + 10x + x + 2x2 + -3x2 = -4 + -1x + 3x2 + 4 + x + -3x2 Combine like terms: 10x + x = 11x 4 + 11x + 2x2 + -3x2 = -4 + -1x + 3x2 + 4 + x + -3x2 Combine like terms: 2x2 + -3x2 = -1x2 4 + 11x + -1x2 = -4 + -1x + 3x2 + 4 + x + -3x2 Reorder the terms: 4 + 11x + -1x2 = -4 + 4 + -1x + x + 3x2 + -3x2 Combine like terms: -4 + 4 = 0 4 + 11x + -1x2 = 0 + -1x + x + 3x2 + -3x2 4 + 11x + -1x2 = -1x + x + 3x2 + -3x2 Combine like terms: -1x + x = 0 4 + 11x + -1x2 = 0 + 3x2 + -3x2 4 + 11x + -1x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 4 + 11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + -11x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -11x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -11x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -11x + x2 = 0 + 4 -11x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -11x + x2 = 4 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 4 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 4 + 30.25 Combine like terms: 4 + 30.25 = 34.25 30.25 + -11x + x2 = 34.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 34.25 Calculate the square root of the right side: 5.852349955 Break this problem into two subproblems by setting (x + -5.5) equal to 5.852349955 and -5.852349955.Subproblem 1
x + -5.5 = 5.852349955 Simplifying x + -5.5 = 5.852349955 Reorder the terms: -5.5 + x = 5.852349955 Solving -5.5 + x = 5.852349955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 5.852349955 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 5.852349955 + 5.5 x = 5.852349955 + 5.5 Combine like terms: 5.852349955 + 5.5 = 11.352349955 x = 11.352349955 Simplifying x = 11.352349955Subproblem 2
x + -5.5 = -5.852349955 Simplifying x + -5.5 = -5.852349955 Reorder the terms: -5.5 + x = -5.852349955 Solving -5.5 + x = -5.852349955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -5.852349955 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -5.852349955 + 5.5 x = -5.852349955 + 5.5 Combine like terms: -5.852349955 + 5.5 = -0.352349955 x = -0.352349955 Simplifying x = -0.352349955Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.352349955, -0.352349955}
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