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Simplifying 3x(2x + 1) + (2x + 5)(2x + -1) + -50x + -25 = 0 Reorder the terms: 3x(1 + 2x) + (2x + 5)(2x + -1) + -50x + -25 = 0 (1 * 3x + 2x * 3x) + (2x + 5)(2x + -1) + -50x + -25 = 0 (3x + 6x2) + (2x + 5)(2x + -1) + -50x + -25 = 0 Reorder the terms: 3x + 6x2 + (5 + 2x)(2x + -1) + -50x + -25 = 0 Reorder the terms: 3x + 6x2 + (5 + 2x)(-1 + 2x) + -50x + -25 = 0 Multiply (5 + 2x) * (-1 + 2x) 3x + 6x2 + (5(-1 + 2x) + 2x * (-1 + 2x)) + -50x + -25 = 0 3x + 6x2 + ((-1 * 5 + 2x * 5) + 2x * (-1 + 2x)) + -50x + -25 = 0 3x + 6x2 + ((-5 + 10x) + 2x * (-1 + 2x)) + -50x + -25 = 0 3x + 6x2 + (-5 + 10x + (-1 * 2x + 2x * 2x)) + -50x + -25 = 0 3x + 6x2 + (-5 + 10x + (-2x + 4x2)) + -50x + -25 = 0 Combine like terms: 10x + -2x = 8x 3x + 6x2 + (-5 + 8x + 4x2) + -50x + -25 = 0 Reorder the terms: -5 + -25 + 3x + 8x + -50x + 6x2 + 4x2 = 0 Combine like terms: -5 + -25 = -30 -30 + 3x + 8x + -50x + 6x2 + 4x2 = 0 Combine like terms: 3x + 8x = 11x -30 + 11x + -50x + 6x2 + 4x2 = 0 Combine like terms: 11x + -50x = -39x -30 + -39x + 6x2 + 4x2 = 0 Combine like terms: 6x2 + 4x2 = 10x2 -30 + -39x + 10x2 = 0 Solving -30 + -39x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -3 + -3.9x + x2 = 0.0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -3.9x + 3 + x2 = 0.0 + 3 Reorder the terms: -3 + 3 + -3.9x + x2 = 0.0 + 3 Combine like terms: -3 + 3 = 0 0 + -3.9x + x2 = 0.0 + 3 -3.9x + x2 = 0.0 + 3 Combine like terms: 0.0 + 3 = 3 -3.9x + x2 = 3 The x term is -3.9x. Take half its coefficient (-1.95). Square it (3.8025) and add it to both sides. Add '3.8025' to each side of the equation. -3.9x + 3.8025 + x2 = 3 + 3.8025 Reorder the terms: 3.8025 + -3.9x + x2 = 3 + 3.8025 Combine like terms: 3 + 3.8025 = 6.8025 3.8025 + -3.9x + x2 = 6.8025 Factor a perfect square on the left side: (x + -1.95)(x + -1.95) = 6.8025 Calculate the square root of the right side: 2.608160271 Break this problem into two subproblems by setting (x + -1.95) equal to 2.608160271 and -2.608160271.Subproblem 1
x + -1.95 = 2.608160271 Simplifying x + -1.95 = 2.608160271 Reorder the terms: -1.95 + x = 2.608160271 Solving -1.95 + x = 2.608160271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.95' to each side of the equation. -1.95 + 1.95 + x = 2.608160271 + 1.95 Combine like terms: -1.95 + 1.95 = 0.00 0.00 + x = 2.608160271 + 1.95 x = 2.608160271 + 1.95 Combine like terms: 2.608160271 + 1.95 = 4.558160271 x = 4.558160271 Simplifying x = 4.558160271Subproblem 2
x + -1.95 = -2.608160271 Simplifying x + -1.95 = -2.608160271 Reorder the terms: -1.95 + x = -2.608160271 Solving -1.95 + x = -2.608160271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.95' to each side of the equation. -1.95 + 1.95 + x = -2.608160271 + 1.95 Combine like terms: -1.95 + 1.95 = 0.00 0.00 + x = -2.608160271 + 1.95 x = -2.608160271 + 1.95 Combine like terms: -2.608160271 + 1.95 = -0.658160271 x = -0.658160271 Simplifying x = -0.658160271Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.558160271, -0.658160271}
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