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Simplifying x(4 + -1x) = x2(7 + -1x) (4 * x + -1x * x) = x2(7 + -1x) (4x + -1x2) = x2(7 + -1x) 4x + -1x2 = (7 * x2 + -1x * x2) 4x + -1x2 = (7x2 + -1x3) Solving 4x + -1x2 = 7x2 + -1x3 Solving for variable 'x'. Combine like terms: -1x2 + -7x2 = -8x2 4x + -8x2 + x3 = 7x2 + -1x3 + -7x2 + x3 Reorder the terms: 4x + -8x2 + x3 = 7x2 + -7x2 + -1x3 + x3 Combine like terms: 7x2 + -7x2 = 0 4x + -8x2 + x3 = 0 + -1x3 + x3 4x + -8x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 4x + -8x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(4 + -8x + x2) = 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 '(4 + -8x + x2)' equal to zero and attempt to solve: Simplifying 4 + -8x + x2 = 0 Solving 4 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -8x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -8x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -8x + x2 = 0 + -4 -8x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -8x + x2 = -4 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -4 + 16 Reorder the terms: 16 + -8x + x2 = -4 + 16 Combine like terms: -4 + 16 = 12 16 + -8x + x2 = 12 Factor a perfect square on the left side: (x + -4)(x + -4) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + -4) equal to 3.464101615 and -3.464101615.Subproblem 1
x + -4 = 3.464101615 Simplifying x + -4 = 3.464101615 Reorder the terms: -4 + x = 3.464101615 Solving -4 + x = 3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 3.464101615 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.464101615 + 4 x = 3.464101615 + 4 Combine like terms: 3.464101615 + 4 = 7.464101615 x = 7.464101615 Simplifying x = 7.464101615Subproblem 2
x + -4 = -3.464101615 Simplifying x + -4 = -3.464101615 Reorder the terms: -4 + x = -3.464101615 Solving -4 + x = -3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -3.464101615 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.464101615 + 4 x = -3.464101615 + 4 Combine like terms: -3.464101615 + 4 = 0.535898385 x = 0.535898385 Simplifying x = 0.535898385Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.464101615, 0.535898385}Solution
x = {0, 7.464101615, 0.535898385}
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