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Simplifying 10 = 128x + -16x2 Solving 10 = 128x + -16x2 Solving for variable 'x'. Reorder the terms: 10 + -128x + 16x2 = 128x + -128x + -16x2 + 16x2 Combine like terms: 128x + -128x = 0 10 + -128x + 16x2 = 0 + -16x2 + 16x2 10 + -128x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 10 + -128x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -64x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -64x + 8x2)' equal to zero and attempt to solve: Simplifying 5 + -64x + 8x2 = 0 Solving 5 + -64x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.625 + -8x + x2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + -8x + -0.625 + x2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + -8x + x2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + -8x + x2 = 0 + -0.625 -8x + x2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 -8x + x2 = -0.625 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -0.625 + 16 Reorder the terms: 16 + -8x + x2 = -0.625 + 16 Combine like terms: -0.625 + 16 = 15.375 16 + -8x + x2 = 15.375 Factor a perfect square on the left side: (x + -4)(x + -4) = 15.375 Calculate the square root of the right side: 3.921096785 Break this problem into two subproblems by setting (x + -4) equal to 3.921096785 and -3.921096785.Subproblem 1
x + -4 = 3.921096785 Simplifying x + -4 = 3.921096785 Reorder the terms: -4 + x = 3.921096785 Solving -4 + x = 3.921096785 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 3.921096785 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.921096785 + 4 x = 3.921096785 + 4 Combine like terms: 3.921096785 + 4 = 7.921096785 x = 7.921096785 Simplifying x = 7.921096785Subproblem 2
x + -4 = -3.921096785 Simplifying x + -4 = -3.921096785 Reorder the terms: -4 + x = -3.921096785 Solving -4 + x = -3.921096785 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -3.921096785 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.921096785 + 4 x = -3.921096785 + 4 Combine like terms: -3.921096785 + 4 = 0.078903215 x = 0.078903215 Simplifying x = 0.078903215Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.921096785, 0.078903215}Solution
x = {7.921096785, 0.078903215}
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