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Simplifying 8x(4x + -5) + -1(3x + 4)(2x + -3) = 2 Reorder the terms: 8x(-5 + 4x) + -1(3x + 4)(2x + -3) = 2 (-5 * 8x + 4x * 8x) + -1(3x + 4)(2x + -3) = 2 (-40x + 32x2) + -1(3x + 4)(2x + -3) = 2 Reorder the terms: -40x + 32x2 + -1(4 + 3x)(2x + -3) = 2 Reorder the terms: -40x + 32x2 + -1(4 + 3x)(-3 + 2x) = 2 Multiply (4 + 3x) * (-3 + 2x) -40x + 32x2 + -1(4(-3 + 2x) + 3x * (-3 + 2x)) = 2 -40x + 32x2 + -1((-3 * 4 + 2x * 4) + 3x * (-3 + 2x)) = 2 -40x + 32x2 + -1((-12 + 8x) + 3x * (-3 + 2x)) = 2 -40x + 32x2 + -1(-12 + 8x + (-3 * 3x + 2x * 3x)) = 2 -40x + 32x2 + -1(-12 + 8x + (-9x + 6x2)) = 2 Combine like terms: 8x + -9x = -1x -40x + 32x2 + -1(-12 + -1x + 6x2) = 2 -40x + 32x2 + (-12 * -1 + -1x * -1 + 6x2 * -1) = 2 -40x + 32x2 + (12 + 1x + -6x2) = 2 Reorder the terms: 12 + -40x + 1x + 32x2 + -6x2 = 2 Combine like terms: -40x + 1x = -39x 12 + -39x + 32x2 + -6x2 = 2 Combine like terms: 32x2 + -6x2 = 26x2 12 + -39x + 26x2 = 2 Solving 12 + -39x + 26x2 = 2 Solving for variable 'x'. Reorder the terms: 12 + -2 + -39x + 26x2 = 2 + -2 Combine like terms: 12 + -2 = 10 10 + -39x + 26x2 = 2 + -2 Combine like terms: 2 + -2 = 0 10 + -39x + 26x2 = 0 Begin completing the square. Divide all terms by 26 the coefficient of the squared term: Divide each side by '26'. 0.3846153846 + -1.5x + x2 = 0 Move the constant term to the right: Add '-0.3846153846' to each side of the equation. 0.3846153846 + -1.5x + -0.3846153846 + x2 = 0 + -0.3846153846 Reorder the terms: 0.3846153846 + -0.3846153846 + -1.5x + x2 = 0 + -0.3846153846 Combine like terms: 0.3846153846 + -0.3846153846 = 0.0000000000 0.0000000000 + -1.5x + x2 = 0 + -0.3846153846 -1.5x + x2 = 0 + -0.3846153846 Combine like terms: 0 + -0.3846153846 = -0.3846153846 -1.5x + x2 = -0.3846153846 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = -0.3846153846 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -0.3846153846 + 0.5625 Combine like terms: -0.3846153846 + 0.5625 = 0.1778846154 0.5625 + -1.5x + x2 = 0.1778846154 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 0.1778846154 Calculate the square root of the right side: 0.421763696 Break this problem into two subproblems by setting (x + -0.75) equal to 0.421763696 and -0.421763696.Subproblem 1
x + -0.75 = 0.421763696 Simplifying x + -0.75 = 0.421763696 Reorder the terms: -0.75 + x = 0.421763696 Solving -0.75 + x = 0.421763696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 0.421763696 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 0.421763696 + 0.75 x = 0.421763696 + 0.75 Combine like terms: 0.421763696 + 0.75 = 1.171763696 x = 1.171763696 Simplifying x = 1.171763696Subproblem 2
x + -0.75 = -0.421763696 Simplifying x + -0.75 = -0.421763696 Reorder the terms: -0.75 + x = -0.421763696 Solving -0.75 + x = -0.421763696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -0.421763696 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -0.421763696 + 0.75 x = -0.421763696 + 0.75 Combine like terms: -0.421763696 + 0.75 = 0.328236304 x = 0.328236304 Simplifying x = 0.328236304Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.171763696, 0.328236304}
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