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Simplifying 8x2 + -4x + 8 = 64 Reorder the terms: 8 + -4x + 8x2 = 64 Solving 8 + -4x + 8x2 = 64 Solving for variable 'x'. Reorder the terms: 8 + -64 + -4x + 8x2 = 64 + -64 Combine like terms: 8 + -64 = -56 -56 + -4x + 8x2 = 64 + -64 Combine like terms: 64 + -64 = 0 -56 + -4x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-14 + -1x + 2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-14 + -1x + 2x2)' equal to zero and attempt to solve: Simplifying -14 + -1x + 2x2 = 0 Solving -14 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7 + -0.5x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -0.5x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -0.5x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -0.5x + x2 = 0 + 7 -0.5x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -0.5x + x2 = 7 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 7 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 7 + 0.0625 Combine like terms: 7 + 0.0625 = 7.0625 0.0625 + -0.5x + x2 = 7.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 7.0625 Calculate the square root of the right side: 2.657536453 Break this problem into two subproblems by setting (x + -0.25) equal to 2.657536453 and -2.657536453.Subproblem 1
x + -0.25 = 2.657536453 Simplifying x + -0.25 = 2.657536453 Reorder the terms: -0.25 + x = 2.657536453 Solving -0.25 + x = 2.657536453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 2.657536453 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 2.657536453 + 0.25 x = 2.657536453 + 0.25 Combine like terms: 2.657536453 + 0.25 = 2.907536453 x = 2.907536453 Simplifying x = 2.907536453Subproblem 2
x + -0.25 = -2.657536453 Simplifying x + -0.25 = -2.657536453 Reorder the terms: -0.25 + x = -2.657536453 Solving -0.25 + x = -2.657536453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -2.657536453 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -2.657536453 + 0.25 x = -2.657536453 + 0.25 Combine like terms: -2.657536453 + 0.25 = -2.407536453 x = -2.407536453 Simplifying x = -2.407536453Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.907536453, -2.407536453}Solution
x = {2.907536453, -2.407536453}
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