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Simplifying 0 = 4x2 + 64x + 71 Reorder the terms: 0 = 71 + 64x + 4x2 Solving 0 = 71 + 64x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -71 = -71 -71 + -64x + -4x2 = 71 + 64x + 4x2 + -71 + -64x + -4x2 Reorder the terms: -71 + -64x + -4x2 = 71 + -71 + 64x + -64x + 4x2 + -4x2 Combine like terms: 71 + -71 = 0 -71 + -64x + -4x2 = 0 + 64x + -64x + 4x2 + -4x2 -71 + -64x + -4x2 = 64x + -64x + 4x2 + -4x2 Combine like terms: 64x + -64x = 0 -71 + -64x + -4x2 = 0 + 4x2 + -4x2 -71 + -64x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -71 + -64x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(71 + 64x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(71 + 64x + 4x2)' equal to zero and attempt to solve: Simplifying 71 + 64x + 4x2 = 0 Solving 71 + 64x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 17.75 + 16x + x2 = 0 Move the constant term to the right: Add '-17.75' to each side of the equation. 17.75 + 16x + -17.75 + x2 = 0 + -17.75 Reorder the terms: 17.75 + -17.75 + 16x + x2 = 0 + -17.75 Combine like terms: 17.75 + -17.75 = 0.00 0.00 + 16x + x2 = 0 + -17.75 16x + x2 = 0 + -17.75 Combine like terms: 0 + -17.75 = -17.75 16x + x2 = -17.75 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = -17.75 + 64 Reorder the terms: 64 + 16x + x2 = -17.75 + 64 Combine like terms: -17.75 + 64 = 46.25 64 + 16x + x2 = 46.25 Factor a perfect square on the left side: (x + 8)(x + 8) = 46.25 Calculate the square root of the right side: 6.800735254 Break this problem into two subproblems by setting (x + 8) equal to 6.800735254 and -6.800735254.Subproblem 1
x + 8 = 6.800735254 Simplifying x + 8 = 6.800735254 Reorder the terms: 8 + x = 6.800735254 Solving 8 + x = 6.800735254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 6.800735254 + -8 Combine like terms: 8 + -8 = 0 0 + x = 6.800735254 + -8 x = 6.800735254 + -8 Combine like terms: 6.800735254 + -8 = -1.199264746 x = -1.199264746 Simplifying x = -1.199264746Subproblem 2
x + 8 = -6.800735254 Simplifying x + 8 = -6.800735254 Reorder the terms: 8 + x = -6.800735254 Solving 8 + x = -6.800735254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -6.800735254 + -8 Combine like terms: 8 + -8 = 0 0 + x = -6.800735254 + -8 x = -6.800735254 + -8 Combine like terms: -6.800735254 + -8 = -14.800735254 x = -14.800735254 Simplifying x = -14.800735254Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.199264746, -14.800735254}Solution
x = {-1.199264746, -14.800735254}
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