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Simplifying -5(2x + 1)(x + 2) = 2 Reorder the terms: -5(1 + 2x)(x + 2) = 2 Reorder the terms: -5(1 + 2x)(2 + x) = 2 Multiply (1 + 2x) * (2 + x) -5(1(2 + x) + 2x * (2 + x)) = 2 -5((2 * 1 + x * 1) + 2x * (2 + x)) = 2 -5((2 + 1x) + 2x * (2 + x)) = 2 -5(2 + 1x + (2 * 2x + x * 2x)) = 2 -5(2 + 1x + (4x + 2x2)) = 2 Combine like terms: 1x + 4x = 5x -5(2 + 5x + 2x2) = 2 (2 * -5 + 5x * -5 + 2x2 * -5) = 2 (-10 + -25x + -10x2) = 2 Solving -10 + -25x + -10x2 = 2 Solving for variable 'x'. Reorder the terms: -10 + -2 + -25x + -10x2 = 2 + -2 Combine like terms: -10 + -2 = -12 -12 + -25x + -10x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -12 + -25x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 25x + 10x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + 25x + 10x2)' equal to zero and attempt to solve: Simplifying 12 + 25x + 10x2 = 0 Solving 12 + 25x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1.2 + 2.5x + x2 = 0.0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + 2.5x + -1.2 + x2 = 0.0 + -1.2 Reorder the terms: 1.2 + -1.2 + 2.5x + x2 = 0.0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + 2.5x + x2 = 0.0 + -1.2 2.5x + x2 = 0.0 + -1.2 Combine like terms: 0.0 + -1.2 = -1.2 2.5x + x2 = -1.2 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = -1.2 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = -1.2 + 1.5625 Combine like terms: -1.2 + 1.5625 = 0.3625 1.5625 + 2.5x + x2 = 0.3625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 0.3625 Calculate the square root of the right side: 0.602079729 Break this problem into two subproblems by setting (x + 1.25) equal to 0.602079729 and -0.602079729.Subproblem 1
x + 1.25 = 0.602079729 Simplifying x + 1.25 = 0.602079729 Reorder the terms: 1.25 + x = 0.602079729 Solving 1.25 + x = 0.602079729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 0.602079729 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 0.602079729 + -1.25 x = 0.602079729 + -1.25 Combine like terms: 0.602079729 + -1.25 = -0.647920271 x = -0.647920271 Simplifying x = -0.647920271Subproblem 2
x + 1.25 = -0.602079729 Simplifying x + 1.25 = -0.602079729 Reorder the terms: 1.25 + x = -0.602079729 Solving 1.25 + x = -0.602079729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -0.602079729 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -0.602079729 + -1.25 x = -0.602079729 + -1.25 Combine like terms: -0.602079729 + -1.25 = -1.852079729 x = -1.852079729 Simplifying x = -1.852079729Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.647920271, -1.852079729}Solution
x = {-0.647920271, -1.852079729}
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