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Simplifying 2x(4x + -4) = 30 + -5x Reorder the terms: 2x(-4 + 4x) = 30 + -5x (-4 * 2x + 4x * 2x) = 30 + -5x (-8x + 8x2) = 30 + -5x Solving -8x + 8x2 = 30 + -5x Solving for variable 'x'. Reorder the terms: -30 + -8x + 5x + 8x2 = 30 + -5x + -30 + 5x Combine like terms: -8x + 5x = -3x -30 + -3x + 8x2 = 30 + -5x + -30 + 5x Reorder the terms: -30 + -3x + 8x2 = 30 + -30 + -5x + 5x Combine like terms: 30 + -30 = 0 -30 + -3x + 8x2 = 0 + -5x + 5x -30 + -3x + 8x2 = -5x + 5x Combine like terms: -5x + 5x = 0 -30 + -3x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3.75 + -0.375x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -0.375x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -0.375x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -0.375x + x2 = 0 + 3.75 -0.375x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -0.375x + x2 = 3.75 The x term is -0.375x. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375x + 0.03515625 + x2 = 3.75 + 0.03515625 Reorder the terms: 0.03515625 + -0.375x + x2 = 3.75 + 0.03515625 Combine like terms: 3.75 + 0.03515625 = 3.78515625 0.03515625 + -0.375x + x2 = 3.78515625 Factor a perfect square on the left side: (x + -0.1875)(x + -0.1875) = 3.78515625 Calculate the square root of the right side: 1.945547802 Break this problem into two subproblems by setting (x + -0.1875) equal to 1.945547802 and -1.945547802.Subproblem 1
x + -0.1875 = 1.945547802 Simplifying x + -0.1875 = 1.945547802 Reorder the terms: -0.1875 + x = 1.945547802 Solving -0.1875 + x = 1.945547802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = 1.945547802 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = 1.945547802 + 0.1875 x = 1.945547802 + 0.1875 Combine like terms: 1.945547802 + 0.1875 = 2.133047802 x = 2.133047802 Simplifying x = 2.133047802Subproblem 2
x + -0.1875 = -1.945547802 Simplifying x + -0.1875 = -1.945547802 Reorder the terms: -0.1875 + x = -1.945547802 Solving -0.1875 + x = -1.945547802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = -1.945547802 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = -1.945547802 + 0.1875 x = -1.945547802 + 0.1875 Combine like terms: -1.945547802 + 0.1875 = -1.758047802 x = -1.758047802 Simplifying x = -1.758047802Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.133047802, -1.758047802}
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