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Simplifying x2 + (2x + -4)(2x + -4) = 25 Reorder the terms: x2 + (-4 + 2x)(2x + -4) = 25 Reorder the terms: x2 + (-4 + 2x)(-4 + 2x) = 25 Multiply (-4 + 2x) * (-4 + 2x) x2 + (-4(-4 + 2x) + 2x * (-4 + 2x)) = 25 x2 + ((-4 * -4 + 2x * -4) + 2x * (-4 + 2x)) = 25 x2 + ((16 + -8x) + 2x * (-4 + 2x)) = 25 x2 + (16 + -8x + (-4 * 2x + 2x * 2x)) = 25 x2 + (16 + -8x + (-8x + 4x2)) = 25 Combine like terms: -8x + -8x = -16x x2 + (16 + -16x + 4x2) = 25 Reorder the terms: 16 + -16x + x2 + 4x2 = 25 Combine like terms: x2 + 4x2 = 5x2 16 + -16x + 5x2 = 25 Solving 16 + -16x + 5x2 = 25 Solving for variable 'x'. Reorder the terms: 16 + -25 + -16x + 5x2 = 25 + -25 Combine like terms: 16 + -25 = -9 -9 + -16x + 5x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -9 + -16x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.8 + -3.2x + x2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + -3.2x + 1.8 + x2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + -3.2x + x2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + -3.2x + x2 = 0 + 1.8 -3.2x + x2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 -3.2x + x2 = 1.8 The x term is -3.2x. Take half its coefficient (-1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. -3.2x + 2.56 + x2 = 1.8 + 2.56 Reorder the terms: 2.56 + -3.2x + x2 = 1.8 + 2.56 Combine like terms: 1.8 + 2.56 = 4.36 2.56 + -3.2x + x2 = 4.36 Factor a perfect square on the left side: (x + -1.6)(x + -1.6) = 4.36 Calculate the square root of the right side: 2.088061302 Break this problem into two subproblems by setting (x + -1.6) equal to 2.088061302 and -2.088061302.Subproblem 1
x + -1.6 = 2.088061302 Simplifying x + -1.6 = 2.088061302 Reorder the terms: -1.6 + x = 2.088061302 Solving -1.6 + x = 2.088061302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = 2.088061302 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = 2.088061302 + 1.6 x = 2.088061302 + 1.6 Combine like terms: 2.088061302 + 1.6 = 3.688061302 x = 3.688061302 Simplifying x = 3.688061302Subproblem 2
x + -1.6 = -2.088061302 Simplifying x + -1.6 = -2.088061302 Reorder the terms: -1.6 + x = -2.088061302 Solving -1.6 + x = -2.088061302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = -2.088061302 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = -2.088061302 + 1.6 x = -2.088061302 + 1.6 Combine like terms: -2.088061302 + 1.6 = -0.488061302 x = -0.488061302 Simplifying x = -0.488061302Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.688061302, -0.488061302}
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