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Simplifying 2x + -5(2x) = (4x + 1)(x + -3) Remove parenthesis around (2x) 2x + -5 * 2x = (4x + 1)(x + -3) Multiply -5 * 2 2x + -10x = (4x + 1)(x + -3) Combine like terms: 2x + -10x = -8x -8x = (4x + 1)(x + -3) Reorder the terms: -8x = (1 + 4x)(x + -3) Reorder the terms: -8x = (1 + 4x)(-3 + x) Multiply (1 + 4x) * (-3 + x) -8x = (1(-3 + x) + 4x * (-3 + x)) -8x = ((-3 * 1 + x * 1) + 4x * (-3 + x)) -8x = ((-3 + 1x) + 4x * (-3 + x)) -8x = (-3 + 1x + (-3 * 4x + x * 4x)) -8x = (-3 + 1x + (-12x + 4x2)) Combine like terms: 1x + -12x = -11x -8x = (-3 + -11x + 4x2) Solving -8x = -3 + -11x + 4x2 Solving for variable 'x'. Reorder the terms: 3 + -8x + 11x + -4x2 = -3 + -11x + 4x2 + 3 + 11x + -4x2 Combine like terms: -8x + 11x = 3x 3 + 3x + -4x2 = -3 + -11x + 4x2 + 3 + 11x + -4x2 Reorder the terms: 3 + 3x + -4x2 = -3 + 3 + -11x + 11x + 4x2 + -4x2 Combine like terms: -3 + 3 = 0 3 + 3x + -4x2 = 0 + -11x + 11x + 4x2 + -4x2 3 + 3x + -4x2 = -11x + 11x + 4x2 + -4x2 Combine like terms: -11x + 11x = 0 3 + 3x + -4x2 = 0 + 4x2 + -4x2 3 + 3x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 3 + 3x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.75 + -0.75x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -0.75x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -0.75x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -0.75x + x2 = 0 + 0.75 -0.75x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -0.75x + x2 = 0.75 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 0.75 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 0.75 + 0.140625 Combine like terms: 0.75 + 0.140625 = 0.890625 0.140625 + -0.75x + x2 = 0.890625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 0.890625 Calculate the square root of the right side: 0.943729304 Break this problem into two subproblems by setting (x + -0.375) equal to 0.943729304 and -0.943729304.Subproblem 1
x + -0.375 = 0.943729304 Simplifying x + -0.375 = 0.943729304 Reorder the terms: -0.375 + x = 0.943729304 Solving -0.375 + x = 0.943729304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 0.943729304 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 0.943729304 + 0.375 x = 0.943729304 + 0.375 Combine like terms: 0.943729304 + 0.375 = 1.318729304 x = 1.318729304 Simplifying x = 1.318729304Subproblem 2
x + -0.375 = -0.943729304 Simplifying x + -0.375 = -0.943729304 Reorder the terms: -0.375 + x = -0.943729304 Solving -0.375 + x = -0.943729304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -0.943729304 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -0.943729304 + 0.375 x = -0.943729304 + 0.375 Combine like terms: -0.943729304 + 0.375 = -0.568729304 x = -0.568729304 Simplifying x = -0.568729304Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.318729304, -0.568729304}
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