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Simplifying 5x(3 + 8 + 3x + -1x) = 19 + -15 + 2x Combine like terms: 3 + 8 = 11 5x(11 + 3x + -1x) = 19 + -15 + 2x Combine like terms: 3x + -1x = 2x 5x(11 + 2x) = 19 + -15 + 2x (11 * 5x + 2x * 5x) = 19 + -15 + 2x (55x + 10x2) = 19 + -15 + 2x Combine like terms: 19 + -15 = 4 55x + 10x2 = 4 + 2x Solving 55x + 10x2 = 4 + 2x Solving for variable 'x'. Reorder the terms: -4 + 55x + -2x + 10x2 = 4 + 2x + -4 + -2x Combine like terms: 55x + -2x = 53x -4 + 53x + 10x2 = 4 + 2x + -4 + -2x Reorder the terms: -4 + 53x + 10x2 = 4 + -4 + 2x + -2x Combine like terms: 4 + -4 = 0 -4 + 53x + 10x2 = 0 + 2x + -2x -4 + 53x + 10x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -4 + 53x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.4 + 5.3x + x2 = 0.0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 5.3x + 0.4 + x2 = 0.0 + 0.4 Reorder the terms: -0.4 + 0.4 + 5.3x + x2 = 0.0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 5.3x + x2 = 0.0 + 0.4 5.3x + x2 = 0.0 + 0.4 Combine like terms: 0.0 + 0.4 = 0.4 5.3x + x2 = 0.4 The x term is 5.3x. Take half its coefficient (2.65). Square it (7.0225) and add it to both sides. Add '7.0225' to each side of the equation. 5.3x + 7.0225 + x2 = 0.4 + 7.0225 Reorder the terms: 7.0225 + 5.3x + x2 = 0.4 + 7.0225 Combine like terms: 0.4 + 7.0225 = 7.4225 7.0225 + 5.3x + x2 = 7.4225 Factor a perfect square on the left side: (x + 2.65)(x + 2.65) = 7.4225 Calculate the square root of the right side: 2.724426545 Break this problem into two subproblems by setting (x + 2.65) equal to 2.724426545 and -2.724426545.Subproblem 1
x + 2.65 = 2.724426545 Simplifying x + 2.65 = 2.724426545 Reorder the terms: 2.65 + x = 2.724426545 Solving 2.65 + x = 2.724426545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.65' to each side of the equation. 2.65 + -2.65 + x = 2.724426545 + -2.65 Combine like terms: 2.65 + -2.65 = 0.00 0.00 + x = 2.724426545 + -2.65 x = 2.724426545 + -2.65 Combine like terms: 2.724426545 + -2.65 = 0.074426545 x = 0.074426545 Simplifying x = 0.074426545Subproblem 2
x + 2.65 = -2.724426545 Simplifying x + 2.65 = -2.724426545 Reorder the terms: 2.65 + x = -2.724426545 Solving 2.65 + x = -2.724426545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.65' to each side of the equation. 2.65 + -2.65 + x = -2.724426545 + -2.65 Combine like terms: 2.65 + -2.65 = 0.00 0.00 + x = -2.724426545 + -2.65 x = -2.724426545 + -2.65 Combine like terms: -2.724426545 + -2.65 = -5.374426545 x = -5.374426545 Simplifying x = -5.374426545Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.074426545, -5.374426545}
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