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Simplifying (5x + -4)(5x + -4) = 32 Reorder the terms: (-4 + 5x)(5x + -4) = 32 Reorder the terms: (-4 + 5x)(-4 + 5x) = 32 Multiply (-4 + 5x) * (-4 + 5x) (-4(-4 + 5x) + 5x * (-4 + 5x)) = 32 ((-4 * -4 + 5x * -4) + 5x * (-4 + 5x)) = 32 ((16 + -20x) + 5x * (-4 + 5x)) = 32 (16 + -20x + (-4 * 5x + 5x * 5x)) = 32 (16 + -20x + (-20x + 25x2)) = 32 Combine like terms: -20x + -20x = -40x (16 + -40x + 25x2) = 32 Solving 16 + -40x + 25x2 = 32 Solving for variable 'x'. Reorder the terms: 16 + -32 + -40x + 25x2 = 32 + -32 Combine like terms: 16 + -32 = -16 -16 + -40x + 25x2 = 32 + -32 Combine like terms: 32 + -32 = 0 -16 + -40x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.64 + -1.6x + x2 = 0 Move the constant term to the right: Add '0.64' to each side of the equation. -0.64 + -1.6x + 0.64 + x2 = 0 + 0.64 Reorder the terms: -0.64 + 0.64 + -1.6x + x2 = 0 + 0.64 Combine like terms: -0.64 + 0.64 = 0.00 0.00 + -1.6x + x2 = 0 + 0.64 -1.6x + x2 = 0 + 0.64 Combine like terms: 0 + 0.64 = 0.64 -1.6x + x2 = 0.64 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = 0.64 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 0.64 + 0.64 Combine like terms: 0.64 + 0.64 = 1.28 0.64 + -1.6x + x2 = 1.28 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 1.28 Calculate the square root of the right side: 1.13137085 Break this problem into two subproblems by setting (x + -0.8) equal to 1.13137085 and -1.13137085.Subproblem 1
x + -0.8 = 1.13137085 Simplifying x + -0.8 = 1.13137085 Reorder the terms: -0.8 + x = 1.13137085 Solving -0.8 + x = 1.13137085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 1.13137085 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 1.13137085 + 0.8 x = 1.13137085 + 0.8 Combine like terms: 1.13137085 + 0.8 = 1.93137085 x = 1.93137085 Simplifying x = 1.93137085Subproblem 2
x + -0.8 = -1.13137085 Simplifying x + -0.8 = -1.13137085 Reorder the terms: -0.8 + x = -1.13137085 Solving -0.8 + x = -1.13137085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -1.13137085 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -1.13137085 + 0.8 x = -1.13137085 + 0.8 Combine like terms: -1.13137085 + 0.8 = -0.33137085 x = -0.33137085 Simplifying x = -0.33137085Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.93137085, -0.33137085}
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