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Simplifying (5x + 6)(5x + -6) = -5x Reorder the terms: (6 + 5x)(5x + -6) = -5x Reorder the terms: (6 + 5x)(-6 + 5x) = -5x Multiply (6 + 5x) * (-6 + 5x) (6(-6 + 5x) + 5x * (-6 + 5x)) = -5x ((-6 * 6 + 5x * 6) + 5x * (-6 + 5x)) = -5x ((-36 + 30x) + 5x * (-6 + 5x)) = -5x (-36 + 30x + (-6 * 5x + 5x * 5x)) = -5x (-36 + 30x + (-30x + 25x2)) = -5x Combine like terms: 30x + -30x = 0 (-36 + 0 + 25x2) = -5x (-36 + 25x2) = -5x Solving -36 + 25x2 = -5x Solving for variable 'x'. Reorder the terms: -36 + 5x + 25x2 = -5x + 5x Combine like terms: -5x + 5x = 0 -36 + 5x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -1.44 + 0.2x + x2 = 0 Move the constant term to the right: Add '1.44' to each side of the equation. -1.44 + 0.2x + 1.44 + x2 = 0 + 1.44 Reorder the terms: -1.44 + 1.44 + 0.2x + x2 = 0 + 1.44 Combine like terms: -1.44 + 1.44 = 0.00 0.00 + 0.2x + x2 = 0 + 1.44 0.2x + x2 = 0 + 1.44 Combine like terms: 0 + 1.44 = 1.44 0.2x + x2 = 1.44 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 = 1.44 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 1.44 + 0.01 Combine like terms: 1.44 + 0.01 = 1.45 0.01 + 0.2x + x2 = 1.45 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 1.45 Calculate the square root of the right side: 1.204159458 Break this problem into two subproblems by setting (x + 0.1) equal to 1.204159458 and -1.204159458.Subproblem 1
x + 0.1 = 1.204159458 Simplifying x + 0.1 = 1.204159458 Reorder the terms: 0.1 + x = 1.204159458 Solving 0.1 + x = 1.204159458 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 = 1.204159458 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 1.204159458 + -0.1 x = 1.204159458 + -0.1 Combine like terms: 1.204159458 + -0.1 = 1.104159458 x = 1.104159458 Simplifying x = 1.104159458Subproblem 2
x + 0.1 = -1.204159458 Simplifying x + 0.1 = -1.204159458 Reorder the terms: 0.1 + x = -1.204159458 Solving 0.1 + x = -1.204159458 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 = -1.204159458 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -1.204159458 + -0.1 x = -1.204159458 + -0.1 Combine like terms: -1.204159458 + -0.1 = -1.304159458 x = -1.304159458 Simplifying x = -1.304159458Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.104159458, -1.304159458}
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