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Simplifying 64x2 + -48x + 9 = 5 Reorder the terms: 9 + -48x + 64x2 = 5 Solving 9 + -48x + 64x2 = 5 Solving for variable 'x'. Reorder the terms: 9 + -5 + -48x + 64x2 = 5 + -5 Combine like terms: 9 + -5 = 4 4 + -48x + 64x2 = 5 + -5 Combine like terms: 5 + -5 = 0 4 + -48x + 64x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(1 + -12x + 16x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -12x + 16x2)' equal to zero and attempt to solve: Simplifying 1 + -12x + 16x2 = 0 Solving 1 + -12x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.0625 + -0.75x + x2 = 0 Move the constant term to the right: Add '-0.0625' to each side of the equation. 0.0625 + -0.75x + -0.0625 + x2 = 0 + -0.0625 Reorder the terms: 0.0625 + -0.0625 + -0.75x + x2 = 0 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + -0.75x + x2 = 0 + -0.0625 -0.75x + x2 = 0 + -0.0625 Combine like terms: 0 + -0.0625 = -0.0625 -0.75x + x2 = -0.0625 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = -0.0625 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = -0.0625 + 0.140625 Combine like terms: -0.0625 + 0.140625 = 0.078125 0.140625 + -0.75x + x2 = 0.078125 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 0.078125 Calculate the square root of the right side: 0.279508497 Break this problem into two subproblems by setting (x + -0.375) equal to 0.279508497 and -0.279508497.Subproblem 1
x + -0.375 = 0.279508497 Simplifying x + -0.375 = 0.279508497 Reorder the terms: -0.375 + x = 0.279508497 Solving -0.375 + x = 0.279508497 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 0.279508497 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 0.279508497 + 0.375 x = 0.279508497 + 0.375 Combine like terms: 0.279508497 + 0.375 = 0.654508497 x = 0.654508497 Simplifying x = 0.654508497Subproblem 2
x + -0.375 = -0.279508497 Simplifying x + -0.375 = -0.279508497 Reorder the terms: -0.375 + x = -0.279508497 Solving -0.375 + x = -0.279508497 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -0.279508497 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -0.279508497 + 0.375 x = -0.279508497 + 0.375 Combine like terms: -0.279508497 + 0.375 = 0.095491503 x = 0.095491503 Simplifying x = 0.095491503Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.654508497, 0.095491503}Solution
x = {0.654508497, 0.095491503}
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