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Simplifying (2x + 3) * 2 = (2x + 1)(7 + -2x) + 74 Reorder the terms: (3 + 2x) * 2 = (2x + 1)(7 + -2x) + 74 Reorder the terms for easier multiplication: 2(3 + 2x) = (2x + 1)(7 + -2x) + 74 (3 * 2 + 2x * 2) = (2x + 1)(7 + -2x) + 74 (6 + 4x) = (2x + 1)(7 + -2x) + 74 Reorder the terms: 6 + 4x = (1 + 2x)(7 + -2x) + 74 Multiply (1 + 2x) * (7 + -2x) 6 + 4x = (1(7 + -2x) + 2x * (7 + -2x)) + 74 6 + 4x = ((7 * 1 + -2x * 1) + 2x * (7 + -2x)) + 74 6 + 4x = ((7 + -2x) + 2x * (7 + -2x)) + 74 6 + 4x = (7 + -2x + (7 * 2x + -2x * 2x)) + 74 6 + 4x = (7 + -2x + (14x + -4x2)) + 74 Combine like terms: -2x + 14x = 12x 6 + 4x = (7 + 12x + -4x2) + 74 Reorder the terms: 6 + 4x = 7 + 74 + 12x + -4x2 Combine like terms: 7 + 74 = 81 6 + 4x = 81 + 12x + -4x2 Solving 6 + 4x = 81 + 12x + -4x2 Solving for variable 'x'. Reorder the terms: 6 + -81 + 4x + -12x + 4x2 = 81 + 12x + -4x2 + -81 + -12x + 4x2 Combine like terms: 6 + -81 = -75 -75 + 4x + -12x + 4x2 = 81 + 12x + -4x2 + -81 + -12x + 4x2 Combine like terms: 4x + -12x = -8x -75 + -8x + 4x2 = 81 + 12x + -4x2 + -81 + -12x + 4x2 Reorder the terms: -75 + -8x + 4x2 = 81 + -81 + 12x + -12x + -4x2 + 4x2 Combine like terms: 81 + -81 = 0 -75 + -8x + 4x2 = 0 + 12x + -12x + -4x2 + 4x2 -75 + -8x + 4x2 = 12x + -12x + -4x2 + 4x2 Combine like terms: 12x + -12x = 0 -75 + -8x + 4x2 = 0 + -4x2 + 4x2 -75 + -8x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -75 + -8x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -18.75 + -2x + x2 = 0 Move the constant term to the right: Add '18.75' to each side of the equation. -18.75 + -2x + 18.75 + x2 = 0 + 18.75 Reorder the terms: -18.75 + 18.75 + -2x + x2 = 0 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + -2x + x2 = 0 + 18.75 -2x + x2 = 0 + 18.75 Combine like terms: 0 + 18.75 = 18.75 -2x + x2 = 18.75 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 18.75 + 1 Reorder the terms: 1 + -2x + x2 = 18.75 + 1 Combine like terms: 18.75 + 1 = 19.75 1 + -2x + x2 = 19.75 Factor a perfect square on the left side: (x + -1)(x + -1) = 19.75 Calculate the square root of the right side: 4.444097209 Break this problem into two subproblems by setting (x + -1) equal to 4.444097209 and -4.444097209.Subproblem 1
x + -1 = 4.444097209 Simplifying x + -1 = 4.444097209 Reorder the terms: -1 + x = 4.444097209 Solving -1 + x = 4.444097209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 4.444097209 + 1 Combine like terms: -1 + 1 = 0 0 + x = 4.444097209 + 1 x = 4.444097209 + 1 Combine like terms: 4.444097209 + 1 = 5.444097209 x = 5.444097209 Simplifying x = 5.444097209Subproblem 2
x + -1 = -4.444097209 Simplifying x + -1 = -4.444097209 Reorder the terms: -1 + x = -4.444097209 Solving -1 + x = -4.444097209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -4.444097209 + 1 Combine like terms: -1 + 1 = 0 0 + x = -4.444097209 + 1 x = -4.444097209 + 1 Combine like terms: -4.444097209 + 1 = -3.444097209 x = -3.444097209 Simplifying x = -3.444097209Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.444097209, -3.444097209}
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