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Simplifying x + -5x(x + 2) = 2x + 4 Reorder the terms: x + -5x(2 + x) = 2x + 4 x + (2 * -5x + x * -5x) = 2x + 4 x + (-10x + -5x2) = 2x + 4 Combine like terms: x + -10x = -9x -9x + -5x2 = 2x + 4 Reorder the terms: -9x + -5x2 = 4 + 2x Solving -9x + -5x2 = 4 + 2x Solving for variable 'x'. Reorder the terms: -4 + -9x + -2x + -5x2 = 4 + 2x + -4 + -2x Combine like terms: -9x + -2x = -11x -4 + -11x + -5x2 = 4 + 2x + -4 + -2x Reorder the terms: -4 + -11x + -5x2 = 4 + -4 + 2x + -2x Combine like terms: 4 + -4 = 0 -4 + -11x + -5x2 = 0 + 2x + -2x -4 + -11x + -5x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -4 + -11x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 11x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 11x + 5x2)' equal to zero and attempt to solve: Simplifying 4 + 11x + 5x2 = 0 Solving 4 + 11x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + 2.2x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + 2.2x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + 2.2x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + 2.2x + x2 = 0 + -0.8 2.2x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 2.2x + x2 = -0.8 The x term is 2.2x. Take half its coefficient (1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. 2.2x + 1.21 + x2 = -0.8 + 1.21 Reorder the terms: 1.21 + 2.2x + x2 = -0.8 + 1.21 Combine like terms: -0.8 + 1.21 = 0.41 1.21 + 2.2x + x2 = 0.41 Factor a perfect square on the left side: (x + 1.1)(x + 1.1) = 0.41 Calculate the square root of the right side: 0.640312424 Break this problem into two subproblems by setting (x + 1.1) equal to 0.640312424 and -0.640312424.Subproblem 1
x + 1.1 = 0.640312424 Simplifying x + 1.1 = 0.640312424 Reorder the terms: 1.1 + x = 0.640312424 Solving 1.1 + x = 0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = 0.640312424 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = 0.640312424 + -1.1 x = 0.640312424 + -1.1 Combine like terms: 0.640312424 + -1.1 = -0.459687576 x = -0.459687576 Simplifying x = -0.459687576Subproblem 2
x + 1.1 = -0.640312424 Simplifying x + 1.1 = -0.640312424 Reorder the terms: 1.1 + x = -0.640312424 Solving 1.1 + x = -0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = -0.640312424 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = -0.640312424 + -1.1 x = -0.640312424 + -1.1 Combine like terms: -0.640312424 + -1.1 = -1.740312424 x = -1.740312424 Simplifying x = -1.740312424Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.459687576, -1.740312424}Solution
x = {-0.459687576, -1.740312424}
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