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Simplifying (2x + -2)(5x + 4) = 2 Reorder the terms: (-2 + 2x)(5x + 4) = 2 Reorder the terms: (-2 + 2x)(4 + 5x) = 2 Multiply (-2 + 2x) * (4 + 5x) (-2(4 + 5x) + 2x * (4 + 5x)) = 2 ((4 * -2 + 5x * -2) + 2x * (4 + 5x)) = 2 ((-8 + -10x) + 2x * (4 + 5x)) = 2 (-8 + -10x + (4 * 2x + 5x * 2x)) = 2 (-8 + -10x + (8x + 10x2)) = 2 Combine like terms: -10x + 8x = -2x (-8 + -2x + 10x2) = 2 Solving -8 + -2x + 10x2 = 2 Solving for variable 'x'. Reorder the terms: -8 + -2 + -2x + 10x2 = 2 + -2 Combine like terms: -8 + -2 = -10 -10 + -2x + 10x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -10 + -2x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -1x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -1x + 5x2)' equal to zero and attempt to solve: Simplifying -5 + -1x + 5x2 = 0 Solving -5 + -1x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1 + -0.2x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.2x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -0.2x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.2x + x2 = 0 + 1 -0.2x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.2x + x2 = 1 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = 1 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 1 + 0.01 Combine like terms: 1 + 0.01 = 1.01 0.01 + -0.2x + x2 = 1.01 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 1.01 Calculate the square root of the right side: 1.004987562 Break this problem into two subproblems by setting (x + -0.1) equal to 1.004987562 and -1.004987562.Subproblem 1
x + -0.1 = 1.004987562 Simplifying x + -0.1 = 1.004987562 Reorder the terms: -0.1 + x = 1.004987562 Solving -0.1 + x = 1.004987562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 1.004987562 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 1.004987562 + 0.1 x = 1.004987562 + 0.1 Combine like terms: 1.004987562 + 0.1 = 1.104987562 x = 1.104987562 Simplifying x = 1.104987562Subproblem 2
x + -0.1 = -1.004987562 Simplifying x + -0.1 = -1.004987562 Reorder the terms: -0.1 + x = -1.004987562 Solving -0.1 + x = -1.004987562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = -1.004987562 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -1.004987562 + 0.1 x = -1.004987562 + 0.1 Combine like terms: -1.004987562 + 0.1 = -0.904987562 x = -0.904987562 Simplifying x = -0.904987562Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.104987562, -0.904987562}Solution
x = {1.104987562, -0.904987562}
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