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Simplifying 4x + -1(2x + 3)(3x + -5) = 49(6x + -1)(x + -2) Reorder the terms: 4x + -1(3 + 2x)(3x + -5) = 49(6x + -1)(x + -2) Reorder the terms: 4x + -1(3 + 2x)(-5 + 3x) = 49(6x + -1)(x + -2) Multiply (3 + 2x) * (-5 + 3x) 4x + -1(3(-5 + 3x) + 2x * (-5 + 3x)) = 49(6x + -1)(x + -2) 4x + -1((-5 * 3 + 3x * 3) + 2x * (-5 + 3x)) = 49(6x + -1)(x + -2) 4x + -1((-15 + 9x) + 2x * (-5 + 3x)) = 49(6x + -1)(x + -2) 4x + -1(-15 + 9x + (-5 * 2x + 3x * 2x)) = 49(6x + -1)(x + -2) 4x + -1(-15 + 9x + (-10x + 6x2)) = 49(6x + -1)(x + -2) Combine like terms: 9x + -10x = -1x 4x + -1(-15 + -1x + 6x2) = 49(6x + -1)(x + -2) 4x + (-15 * -1 + -1x * -1 + 6x2 * -1) = 49(6x + -1)(x + -2) 4x + (15 + 1x + -6x2) = 49(6x + -1)(x + -2) Reorder the terms: 15 + 4x + 1x + -6x2 = 49(6x + -1)(x + -2) Combine like terms: 4x + 1x = 5x 15 + 5x + -6x2 = 49(6x + -1)(x + -2) Reorder the terms: 15 + 5x + -6x2 = 49(-1 + 6x)(x + -2) Reorder the terms: 15 + 5x + -6x2 = 49(-1 + 6x)(-2 + x) Multiply (-1 + 6x) * (-2 + x) 15 + 5x + -6x2 = 49(-1(-2 + x) + 6x * (-2 + x)) 15 + 5x + -6x2 = 49((-2 * -1 + x * -1) + 6x * (-2 + x)) 15 + 5x + -6x2 = 49((2 + -1x) + 6x * (-2 + x)) 15 + 5x + -6x2 = 49(2 + -1x + (-2 * 6x + x * 6x)) 15 + 5x + -6x2 = 49(2 + -1x + (-12x + 6x2)) Combine like terms: -1x + -12x = -13x 15 + 5x + -6x2 = 49(2 + -13x + 6x2) 15 + 5x + -6x2 = (2 * 49 + -13x * 49 + 6x2 * 49) 15 + 5x + -6x2 = (98 + -637x + 294x2) Solving 15 + 5x + -6x2 = 98 + -637x + 294x2 Solving for variable 'x'. Reorder the terms: 15 + -98 + 5x + 637x + -6x2 + -294x2 = 98 + -637x + 294x2 + -98 + 637x + -294x2 Combine like terms: 15 + -98 = -83 -83 + 5x + 637x + -6x2 + -294x2 = 98 + -637x + 294x2 + -98 + 637x + -294x2 Combine like terms: 5x + 637x = 642x -83 + 642x + -6x2 + -294x2 = 98 + -637x + 294x2 + -98 + 637x + -294x2 Combine like terms: -6x2 + -294x2 = -300x2 -83 + 642x + -300x2 = 98 + -637x + 294x2 + -98 + 637x + -294x2 Reorder the terms: -83 + 642x + -300x2 = 98 + -98 + -637x + 637x + 294x2 + -294x2 Combine like terms: 98 + -98 = 0 -83 + 642x + -300x2 = 0 + -637x + 637x + 294x2 + -294x2 -83 + 642x + -300x2 = -637x + 637x + 294x2 + -294x2 Combine like terms: -637x + 637x = 0 -83 + 642x + -300x2 = 0 + 294x2 + -294x2 -83 + 642x + -300x2 = 294x2 + -294x2 Combine like terms: 294x2 + -294x2 = 0 -83 + 642x + -300x2 = 0 Begin completing the square. Divide all terms by -300 the coefficient of the squared term: Divide each side by '-300'. 0.2766666667 + -2.14x + x2 = 0.00 Move the constant term to the right: Add '-0.2766666667' to each side of the equation. 0.2766666667 + -2.14x + -0.2766666667 + x2 = 0.00 + -0.2766666667 Reorder the terms: 0.2766666667 + -0.2766666667 + -2.14x + x2 = 0.00 + -0.2766666667 Combine like terms: 0.2766666667 + -0.2766666667 = 0.0000000000 0.0000000000 + -2.14x + x2 = 0.00 + -0.2766666667 -2.14x + x2 = 0.00 + -0.2766666667 Combine like terms: 0.00 + -0.2766666667 = -0.2766666667 -2.14x + x2 = -0.2766666667 The x term is -2.14x. Take half its coefficient (-1.07). Square it (1.1449) and add it to both sides. Add '1.1449' to each side of the equation. -2.14x + 1.1449 + x2 = -0.2766666667 + 1.1449 Reorder the terms: 1.1449 + -2.14x + x2 = -0.2766666667 + 1.1449 Combine like terms: -0.2766666667 + 1.1449 = 0.8682333333 1.1449 + -2.14x + x2 = 0.8682333333 Factor a perfect square on the left side: (x + -1.07)(x + -1.07) = 0.8682333333 Calculate the square root of the right side: 0.931790391 Break this problem into two subproblems by setting (x + -1.07) equal to 0.931790391 and -0.931790391.Subproblem 1
x + -1.07 = 0.931790391 Simplifying x + -1.07 = 0.931790391 Reorder the terms: -1.07 + x = 0.931790391 Solving -1.07 + x = 0.931790391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.07' to each side of the equation. -1.07 + 1.07 + x = 0.931790391 + 1.07 Combine like terms: -1.07 + 1.07 = 0.00 0.00 + x = 0.931790391 + 1.07 x = 0.931790391 + 1.07 Combine like terms: 0.931790391 + 1.07 = 2.001790391 x = 2.001790391 Simplifying x = 2.001790391Subproblem 2
x + -1.07 = -0.931790391 Simplifying x + -1.07 = -0.931790391 Reorder the terms: -1.07 + x = -0.931790391 Solving -1.07 + x = -0.931790391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.07' to each side of the equation. -1.07 + 1.07 + x = -0.931790391 + 1.07 Combine like terms: -1.07 + 1.07 = 0.00 0.00 + x = -0.931790391 + 1.07 x = -0.931790391 + 1.07 Combine like terms: -0.931790391 + 1.07 = 0.138209609 x = 0.138209609 Simplifying x = 0.138209609Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.001790391, 0.138209609}
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