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Simplifying 56 = 2x2 + 4x(4) Reorder the terms for easier multiplication: 56 = 2x2 + 4 * 4x Multiply 4 * 4 56 = 2x2 + 16x Reorder the terms: 56 = 16x + 2x2 Solving 56 = 16x + 2x2 Solving for variable 'x'. Reorder the terms: 56 + -16x + -2x2 = 16x + -16x + 2x2 + -2x2 Combine like terms: 16x + -16x = 0 56 + -16x + -2x2 = 0 + 2x2 + -2x2 56 + -16x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 56 + -16x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(28 + -8x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(28 + -8x + -1x2)' equal to zero and attempt to solve: Simplifying 28 + -8x + -1x2 = 0 Solving 28 + -8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -28 + 8x + x2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + 8x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + 8x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 8x + x2 = 0 + 28 8x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 8x + x2 = 28 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 = 28 + 16 Reorder the terms: 16 + 8x + x2 = 28 + 16 Combine like terms: 28 + 16 = 44 16 + 8x + x2 = 44 Factor a perfect square on the left side: (x + 4)(x + 4) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (x + 4) equal to 6.633249581 and -6.633249581.Subproblem 1
x + 4 = 6.633249581 Simplifying x + 4 = 6.633249581 Reorder the terms: 4 + x = 6.633249581 Solving 4 + x = 6.633249581 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 = 6.633249581 + -4 Combine like terms: 4 + -4 = 0 0 + x = 6.633249581 + -4 x = 6.633249581 + -4 Combine like terms: 6.633249581 + -4 = 2.633249581 x = 2.633249581 Simplifying x = 2.633249581Subproblem 2
x + 4 = -6.633249581 Simplifying x + 4 = -6.633249581 Reorder the terms: 4 + x = -6.633249581 Solving 4 + x = -6.633249581 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 = -6.633249581 + -4 Combine like terms: 4 + -4 = 0 0 + x = -6.633249581 + -4 x = -6.633249581 + -4 Combine like terms: -6.633249581 + -4 = -10.633249581 x = -10.633249581 Simplifying x = -10.633249581Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.633249581, -10.633249581}Solution
x = {2.633249581, -10.633249581}
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