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Simplifying 8x(-2x + 6) = 4x + -48 Reorder the terms: 8x(6 + -2x) = 4x + -48 (6 * 8x + -2x * 8x) = 4x + -48 (48x + -16x2) = 4x + -48 Reorder the terms: 48x + -16x2 = -48 + 4x Solving 48x + -16x2 = -48 + 4x Solving for variable 'x'. Reorder the terms: 48 + 48x + -4x + -16x2 = -48 + 4x + 48 + -4x Combine like terms: 48x + -4x = 44x 48 + 44x + -16x2 = -48 + 4x + 48 + -4x Reorder the terms: 48 + 44x + -16x2 = -48 + 48 + 4x + -4x Combine like terms: -48 + 48 = 0 48 + 44x + -16x2 = 0 + 4x + -4x 48 + 44x + -16x2 = 4x + -4x Combine like terms: 4x + -4x = 0 48 + 44x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(12 + 11x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(12 + 11x + -4x2)' equal to zero and attempt to solve: Simplifying 12 + 11x + -4x2 = 0 Solving 12 + 11x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -3 + -2.75x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -2.75x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -2.75x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2.75x + x2 = 0 + 3 -2.75x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -2.75x + x2 = 3 The x term is -2.75x. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75x + 1.890625 + x2 = 3 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 3 + 1.890625 Combine like terms: 3 + 1.890625 = 4.890625 1.890625 + -2.75x + x2 = 4.890625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 4.890625 Calculate the square root of the right side: 2.211475752 Break this problem into two subproblems by setting (x + -1.375) equal to 2.211475752 and -2.211475752.Subproblem 1
x + -1.375 = 2.211475752 Simplifying x + -1.375 = 2.211475752 Reorder the terms: -1.375 + x = 2.211475752 Solving -1.375 + x = 2.211475752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = 2.211475752 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 2.211475752 + 1.375 x = 2.211475752 + 1.375 Combine like terms: 2.211475752 + 1.375 = 3.586475752 x = 3.586475752 Simplifying x = 3.586475752Subproblem 2
x + -1.375 = -2.211475752 Simplifying x + -1.375 = -2.211475752 Reorder the terms: -1.375 + x = -2.211475752 Solving -1.375 + x = -2.211475752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = -2.211475752 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -2.211475752 + 1.375 x = -2.211475752 + 1.375 Combine like terms: -2.211475752 + 1.375 = -0.836475752 x = -0.836475752 Simplifying x = -0.836475752Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.586475752, -0.836475752}Solution
x = {3.586475752, -0.836475752}
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