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Simplifying 8x2 + -16x = 68 Reorder the terms: -16x + 8x2 = 68 Solving -16x + 8x2 = 68 Solving for variable 'x'. Reorder the terms: -68 + -16x + 8x2 = 68 + -68 Combine like terms: 68 + -68 = 0 -68 + -16x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-17 + -4x + 2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-17 + -4x + 2x2)' equal to zero and attempt to solve: Simplifying -17 + -4x + 2x2 = 0 Solving -17 + -4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -8.5 + -2x + x2 = 0 Move the constant term to the right: Add '8.5' to each side of the equation. -8.5 + -2x + 8.5 + x2 = 0 + 8.5 Reorder the terms: -8.5 + 8.5 + -2x + x2 = 0 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + -2x + x2 = 0 + 8.5 -2x + x2 = 0 + 8.5 Combine like terms: 0 + 8.5 = 8.5 -2x + x2 = 8.5 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 = 8.5 + 1 Reorder the terms: 1 + -2x + x2 = 8.5 + 1 Combine like terms: 8.5 + 1 = 9.5 1 + -2x + x2 = 9.5 Factor a perfect square on the left side: (x + -1)(x + -1) = 9.5 Calculate the square root of the right side: 3.082207001 Break this problem into two subproblems by setting (x + -1) equal to 3.082207001 and -3.082207001.Subproblem 1
x + -1 = 3.082207001 Simplifying x + -1 = 3.082207001 Reorder the terms: -1 + x = 3.082207001 Solving -1 + x = 3.082207001 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 = 3.082207001 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.082207001 + 1 x = 3.082207001 + 1 Combine like terms: 3.082207001 + 1 = 4.082207001 x = 4.082207001 Simplifying x = 4.082207001Subproblem 2
x + -1 = -3.082207001 Simplifying x + -1 = -3.082207001 Reorder the terms: -1 + x = -3.082207001 Solving -1 + x = -3.082207001 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 = -3.082207001 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.082207001 + 1 x = -3.082207001 + 1 Combine like terms: -3.082207001 + 1 = -2.082207001 x = -2.082207001 Simplifying x = -2.082207001Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.082207001, -2.082207001}Solution
x = {4.082207001, -2.082207001}
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