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Simplifying 2x2(x + -3) = 8x2 + -7x Reorder the terms: 2x2(-3 + x) = 8x2 + -7x (-3 * 2x2 + x * 2x2) = 8x2 + -7x (-6x2 + 2x3) = 8x2 + -7x Reorder the terms: -6x2 + 2x3 = -7x + 8x2 Solving -6x2 + 2x3 = -7x + 8x2 Solving for variable 'x'. Reorder the terms: 7x + -6x2 + -8x2 + 2x3 = -7x + 8x2 + 7x + -8x2 Combine like terms: -6x2 + -8x2 = -14x2 7x + -14x2 + 2x3 = -7x + 8x2 + 7x + -8x2 Reorder the terms: 7x + -14x2 + 2x3 = -7x + 7x + 8x2 + -8x2 Combine like terms: -7x + 7x = 0 7x + -14x2 + 2x3 = 0 + 8x2 + -8x2 7x + -14x2 + 2x3 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 7x + -14x2 + 2x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(7 + -14x + 2x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(7 + -14x + 2x2)' equal to zero and attempt to solve: Simplifying 7 + -14x + 2x2 = 0 Solving 7 + -14x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + -7x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -7x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -7x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -7x + x2 = 0 + -3.5 -7x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -7x + x2 = -3.5 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -3.5 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -3.5 + 12.25 Combine like terms: -3.5 + 12.25 = 8.75 12.25 + -7x + x2 = 8.75 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 8.75 Calculate the square root of the right side: 2.958039892 Break this problem into two subproblems by setting (x + -3.5) equal to 2.958039892 and -2.958039892.Subproblem 1
x + -3.5 = 2.958039892 Simplifying x + -3.5 = 2.958039892 Reorder the terms: -3.5 + x = 2.958039892 Solving -3.5 + x = 2.958039892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 2.958039892 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 2.958039892 + 3.5 x = 2.958039892 + 3.5 Combine like terms: 2.958039892 + 3.5 = 6.458039892 x = 6.458039892 Simplifying x = 6.458039892Subproblem 2
x + -3.5 = -2.958039892 Simplifying x + -3.5 = -2.958039892 Reorder the terms: -3.5 + x = -2.958039892 Solving -3.5 + x = -2.958039892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -2.958039892 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -2.958039892 + 3.5 x = -2.958039892 + 3.5 Combine like terms: -2.958039892 + 3.5 = 0.541960108 x = 0.541960108 Simplifying x = 0.541960108Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.458039892, 0.541960108}Solution
x = {0, 6.458039892, 0.541960108}
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