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Simplifying 8x2 + 16x = 52 Reorder the terms: 16x + 8x2 = 52 Solving 16x + 8x2 = 52 Solving for variable 'x'. Reorder the terms: -52 + 16x + 8x2 = 52 + -52 Combine like terms: 52 + -52 = 0 -52 + 16x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-13 + 4x + 2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-13 + 4x + 2x2)' equal to zero and attempt to solve: Simplifying -13 + 4x + 2x2 = 0 Solving -13 + 4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6.5 + 2x + x2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + 2x + 6.5 + x2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + 2x + x2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + 2x + x2 = 0 + 6.5 2x + x2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 2x + x2 = 6.5 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 6.5 + 1 Reorder the terms: 1 + 2x + x2 = 6.5 + 1 Combine like terms: 6.5 + 1 = 7.5 1 + 2x + x2 = 7.5 Factor a perfect square on the left side: (x + 1)(x + 1) = 7.5 Calculate the square root of the right side: 2.738612788 Break this problem into two subproblems by setting (x + 1) equal to 2.738612788 and -2.738612788.Subproblem 1
x + 1 = 2.738612788 Simplifying x + 1 = 2.738612788 Reorder the terms: 1 + x = 2.738612788 Solving 1 + x = 2.738612788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.738612788 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.738612788 + -1 x = 2.738612788 + -1 Combine like terms: 2.738612788 + -1 = 1.738612788 x = 1.738612788 Simplifying x = 1.738612788Subproblem 2
x + 1 = -2.738612788 Simplifying x + 1 = -2.738612788 Reorder the terms: 1 + x = -2.738612788 Solving 1 + x = -2.738612788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.738612788 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.738612788 + -1 x = -2.738612788 + -1 Combine like terms: -2.738612788 + -1 = -3.738612788 x = -3.738612788 Simplifying x = -3.738612788Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.738612788, -3.738612788}Solution
x = {1.738612788, -3.738612788}
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