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Simplifying (2x + -4)(2x + -4) = 75 Reorder the terms: (-4 + 2x)(2x + -4) = 75 Reorder the terms: (-4 + 2x)(-4 + 2x) = 75 Multiply (-4 + 2x) * (-4 + 2x) (-4(-4 + 2x) + 2x * (-4 + 2x)) = 75 ((-4 * -4 + 2x * -4) + 2x * (-4 + 2x)) = 75 ((16 + -8x) + 2x * (-4 + 2x)) = 75 (16 + -8x + (-4 * 2x + 2x * 2x)) = 75 (16 + -8x + (-8x + 4x2)) = 75 Combine like terms: -8x + -8x = -16x (16 + -16x + 4x2) = 75 Solving 16 + -16x + 4x2 = 75 Solving for variable 'x'. Reorder the terms: 16 + -75 + -16x + 4x2 = 75 + -75 Combine like terms: 16 + -75 = -59 -59 + -16x + 4x2 = 75 + -75 Combine like terms: 75 + -75 = 0 -59 + -16x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -14.75 + -4x + x2 = 0 Move the constant term to the right: Add '14.75' to each side of the equation. -14.75 + -4x + 14.75 + x2 = 0 + 14.75 Reorder the terms: -14.75 + 14.75 + -4x + x2 = 0 + 14.75 Combine like terms: -14.75 + 14.75 = 0.00 0.00 + -4x + x2 = 0 + 14.75 -4x + x2 = 0 + 14.75 Combine like terms: 0 + 14.75 = 14.75 -4x + x2 = 14.75 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 14.75 + 4 Reorder the terms: 4 + -4x + x2 = 14.75 + 4 Combine like terms: 14.75 + 4 = 18.75 4 + -4x + x2 = 18.75 Factor a perfect square on the left side: (x + -2)(x + -2) = 18.75 Calculate the square root of the right side: 4.330127019 Break this problem into two subproblems by setting (x + -2) equal to 4.330127019 and -4.330127019.Subproblem 1
x + -2 = 4.330127019 Simplifying x + -2 = 4.330127019 Reorder the terms: -2 + x = 4.330127019 Solving -2 + x = 4.330127019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 4.330127019 + 2 Combine like terms: -2 + 2 = 0 0 + x = 4.330127019 + 2 x = 4.330127019 + 2 Combine like terms: 4.330127019 + 2 = 6.330127019 x = 6.330127019 Simplifying x = 6.330127019Subproblem 2
x + -2 = -4.330127019 Simplifying x + -2 = -4.330127019 Reorder the terms: -2 + x = -4.330127019 Solving -2 + x = -4.330127019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -4.330127019 + 2 Combine like terms: -2 + 2 = 0 0 + x = -4.330127019 + 2 x = -4.330127019 + 2 Combine like terms: -4.330127019 + 2 = -2.330127019 x = -2.330127019 Simplifying x = -2.330127019Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.330127019, -2.330127019}
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