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Simplifying 5x(x + 11) + 2(2x + -5) = 0 Reorder the terms: 5x(11 + x) + 2(2x + -5) = 0 (11 * 5x + x * 5x) + 2(2x + -5) = 0 (55x + 5x2) + 2(2x + -5) = 0 Reorder the terms: 55x + 5x2 + 2(-5 + 2x) = 0 55x + 5x2 + (-5 * 2 + 2x * 2) = 0 55x + 5x2 + (-10 + 4x) = 0 Reorder the terms: -10 + 55x + 4x + 5x2 = 0 Combine like terms: 55x + 4x = 59x -10 + 59x + 5x2 = 0 Solving -10 + 59x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2 + 11.8x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 11.8x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 11.8x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 11.8x + x2 = 0 + 2 11.8x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 11.8x + x2 = 2 The x term is 11.8x. Take half its coefficient (5.9). Square it (34.81) and add it to both sides. Add '34.81' to each side of the equation. 11.8x + 34.81 + x2 = 2 + 34.81 Reorder the terms: 34.81 + 11.8x + x2 = 2 + 34.81 Combine like terms: 2 + 34.81 = 36.81 34.81 + 11.8x + x2 = 36.81 Factor a perfect square on the left side: (x + 5.9)(x + 5.9) = 36.81 Calculate the square root of the right side: 6.067124525 Break this problem into two subproblems by setting (x + 5.9) equal to 6.067124525 and -6.067124525.Subproblem 1
x + 5.9 = 6.067124525 Simplifying x + 5.9 = 6.067124525 Reorder the terms: 5.9 + x = 6.067124525 Solving 5.9 + x = 6.067124525 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.9' to each side of the equation. 5.9 + -5.9 + x = 6.067124525 + -5.9 Combine like terms: 5.9 + -5.9 = 0.0 0.0 + x = 6.067124525 + -5.9 x = 6.067124525 + -5.9 Combine like terms: 6.067124525 + -5.9 = 0.167124525 x = 0.167124525 Simplifying x = 0.167124525Subproblem 2
x + 5.9 = -6.067124525 Simplifying x + 5.9 = -6.067124525 Reorder the terms: 5.9 + x = -6.067124525 Solving 5.9 + x = -6.067124525 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.9' to each side of the equation. 5.9 + -5.9 + x = -6.067124525 + -5.9 Combine like terms: 5.9 + -5.9 = 0.0 0.0 + x = -6.067124525 + -5.9 x = -6.067124525 + -5.9 Combine like terms: -6.067124525 + -5.9 = -11.967124525 x = -11.967124525 Simplifying x = -11.967124525Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.167124525, -11.967124525}
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