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Simplifying (x + -2)(4x + 1) + -1(2x + 3) * 2 = 8 Reorder the terms: (-2 + x)(4x + 1) + -1(2x + 3) * 2 = 8 Reorder the terms: (-2 + x)(1 + 4x) + -1(2x + 3) * 2 = 8 Multiply (-2 + x) * (1 + 4x) (-2(1 + 4x) + x(1 + 4x)) + -1(2x + 3) * 2 = 8 ((1 * -2 + 4x * -2) + x(1 + 4x)) + -1(2x + 3) * 2 = 8 ((-2 + -8x) + x(1 + 4x)) + -1(2x + 3) * 2 = 8 (-2 + -8x + (1 * x + 4x * x)) + -1(2x + 3) * 2 = 8 (-2 + -8x + (1x + 4x2)) + -1(2x + 3) * 2 = 8 Combine like terms: -8x + 1x = -7x (-2 + -7x + 4x2) + -1(2x + 3) * 2 = 8 Reorder the terms: -2 + -7x + 4x2 + -1(3 + 2x) * 2 = 8 Reorder the terms for easier multiplication: -2 + -7x + 4x2 + -1 * 2(3 + 2x) = 8 Multiply -1 * 2 -2 + -7x + 4x2 + -2(3 + 2x) = 8 -2 + -7x + 4x2 + (3 * -2 + 2x * -2) = 8 -2 + -7x + 4x2 + (-6 + -4x) = 8 Reorder the terms: -2 + -6 + -7x + -4x + 4x2 = 8 Combine like terms: -2 + -6 = -8 -8 + -7x + -4x + 4x2 = 8 Combine like terms: -7x + -4x = -11x -8 + -11x + 4x2 = 8 Solving -8 + -11x + 4x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + -8 + -11x + 4x2 = 8 + -8 Combine like terms: -8 + -8 = -16 -16 + -11x + 4x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -16 + -11x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4 + -2.75x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -2.75x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -2.75x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -2.75x + x2 = 0 + 4 -2.75x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -2.75x + x2 = 4 The x term is -2.75x. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75x + 1.890625 + x2 = 4 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 4 + 1.890625 Combine like terms: 4 + 1.890625 = 5.890625 1.890625 + -2.75x + x2 = 5.890625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 5.890625 Calculate the square root of the right side: 2.42706098 Break this problem into two subproblems by setting (x + -1.375) equal to 2.42706098 and -2.42706098.Subproblem 1
x + -1.375 = 2.42706098 Simplifying x + -1.375 = 2.42706098 Reorder the terms: -1.375 + x = 2.42706098 Solving -1.375 + x = 2.42706098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = 2.42706098 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 2.42706098 + 1.375 x = 2.42706098 + 1.375 Combine like terms: 2.42706098 + 1.375 = 3.80206098 x = 3.80206098 Simplifying x = 3.80206098Subproblem 2
x + -1.375 = -2.42706098 Simplifying x + -1.375 = -2.42706098 Reorder the terms: -1.375 + x = -2.42706098 Solving -1.375 + x = -2.42706098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = -2.42706098 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -2.42706098 + 1.375 x = -2.42706098 + 1.375 Combine like terms: -2.42706098 + 1.375 = -1.05206098 x = -1.05206098 Simplifying x = -1.05206098Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.80206098, -1.05206098}
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