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Simplifying -6(3x + -1)(3x + 1) + -5(2x + 1)(x + -4) = 3 Reorder the terms: -6(-1 + 3x)(3x + 1) + -5(2x + 1)(x + -4) = 3 Reorder the terms: -6(-1 + 3x)(1 + 3x) + -5(2x + 1)(x + -4) = 3 Multiply (-1 + 3x) * (1 + 3x) -6(-1(1 + 3x) + 3x * (1 + 3x)) + -5(2x + 1)(x + -4) = 3 -6((1 * -1 + 3x * -1) + 3x * (1 + 3x)) + -5(2x + 1)(x + -4) = 3 -6((-1 + -3x) + 3x * (1 + 3x)) + -5(2x + 1)(x + -4) = 3 -6(-1 + -3x + (1 * 3x + 3x * 3x)) + -5(2x + 1)(x + -4) = 3 -6(-1 + -3x + (3x + 9x2)) + -5(2x + 1)(x + -4) = 3 Combine like terms: -3x + 3x = 0 -6(-1 + 0 + 9x2) + -5(2x + 1)(x + -4) = 3 -6(-1 + 9x2) + -5(2x + 1)(x + -4) = 3 (-1 * -6 + 9x2 * -6) + -5(2x + 1)(x + -4) = 3 (6 + -54x2) + -5(2x + 1)(x + -4) = 3 Reorder the terms: 6 + -54x2 + -5(1 + 2x)(x + -4) = 3 Reorder the terms: 6 + -54x2 + -5(1 + 2x)(-4 + x) = 3 Multiply (1 + 2x) * (-4 + x) 6 + -54x2 + -5(1(-4 + x) + 2x * (-4 + x)) = 3 6 + -54x2 + -5((-4 * 1 + x * 1) + 2x * (-4 + x)) = 3 6 + -54x2 + -5((-4 + 1x) + 2x * (-4 + x)) = 3 6 + -54x2 + -5(-4 + 1x + (-4 * 2x + x * 2x)) = 3 6 + -54x2 + -5(-4 + 1x + (-8x + 2x2)) = 3 Combine like terms: 1x + -8x = -7x 6 + -54x2 + -5(-4 + -7x + 2x2) = 3 6 + -54x2 + (-4 * -5 + -7x * -5 + 2x2 * -5) = 3 6 + -54x2 + (20 + 35x + -10x2) = 3 Reorder the terms: 6 + 20 + 35x + -54x2 + -10x2 = 3 Combine like terms: 6 + 20 = 26 26 + 35x + -54x2 + -10x2 = 3 Combine like terms: -54x2 + -10x2 = -64x2 26 + 35x + -64x2 = 3 Solving 26 + 35x + -64x2 = 3 Solving for variable 'x'. Reorder the terms: 26 + -3 + 35x + -64x2 = 3 + -3 Combine like terms: 26 + -3 = 23 23 + 35x + -64x2 = 3 + -3 Combine like terms: 3 + -3 = 0 23 + 35x + -64x2 = 0 Begin completing the square. Divide all terms by -64 the coefficient of the squared term: Divide each side by '-64'. -0.359375 + -0.546875x + x2 = 0 Move the constant term to the right: Add '0.359375' to each side of the equation. -0.359375 + -0.546875x + 0.359375 + x2 = 0 + 0.359375 Reorder the terms: -0.359375 + 0.359375 + -0.546875x + x2 = 0 + 0.359375 Combine like terms: -0.359375 + 0.359375 = 0.000000 0.000000 + -0.546875x + x2 = 0 + 0.359375 -0.546875x + x2 = 0 + 0.359375 Combine like terms: 0 + 0.359375 = 0.359375 -0.546875x + x2 = 0.359375 The x term is -0.546875x. Take half its coefficient (-0.2734375). Square it (0.07476806641) and add it to both sides. Add '0.07476806641' to each side of the equation. -0.546875x + 0.07476806641 + x2 = 0.359375 + 0.07476806641 Reorder the terms: 0.07476806641 + -0.546875x + x2 = 0.359375 + 0.07476806641 Combine like terms: 0.359375 + 0.07476806641 = 0.43414306641 0.07476806641 + -0.546875x + x2 = 0.43414306641 Factor a perfect square on the left side: (x + -0.2734375)(x + -0.2734375) = 0.43414306641 Calculate the square root of the right side: 0.658895338 Break this problem into two subproblems by setting (x + -0.2734375) equal to 0.658895338 and -0.658895338.Subproblem 1
x + -0.2734375 = 0.658895338 Simplifying x + -0.2734375 = 0.658895338 Reorder the terms: -0.2734375 + x = 0.658895338 Solving -0.2734375 + x = 0.658895338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2734375' to each side of the equation. -0.2734375 + 0.2734375 + x = 0.658895338 + 0.2734375 Combine like terms: -0.2734375 + 0.2734375 = 0.0000000 0.0000000 + x = 0.658895338 + 0.2734375 x = 0.658895338 + 0.2734375 Combine like terms: 0.658895338 + 0.2734375 = 0.932332838 x = 0.932332838 Simplifying x = 0.932332838Subproblem 2
x + -0.2734375 = -0.658895338 Simplifying x + -0.2734375 = -0.658895338 Reorder the terms: -0.2734375 + x = -0.658895338 Solving -0.2734375 + x = -0.658895338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2734375' to each side of the equation. -0.2734375 + 0.2734375 + x = -0.658895338 + 0.2734375 Combine like terms: -0.2734375 + 0.2734375 = 0.0000000 0.0000000 + x = -0.658895338 + 0.2734375 x = -0.658895338 + 0.2734375 Combine like terms: -0.658895338 + 0.2734375 = -0.385457838 x = -0.385457838 Simplifying x = -0.385457838Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.932332838, -0.385457838}
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