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Simplifying 64x2 + 16x = 14 Reorder the terms: 16x + 64x2 = 14 Solving 16x + 64x2 = 14 Solving for variable 'x'. Reorder the terms: -14 + 16x + 64x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + 16x + 64x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 8x + 32x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + 8x + 32x2)' equal to zero and attempt to solve: Simplifying -7 + 8x + 32x2 = 0 Solving -7 + 8x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -0.21875 + 0.25x + x2 = 0 Move the constant term to the right: Add '0.21875' to each side of the equation. -0.21875 + 0.25x + 0.21875 + x2 = 0 + 0.21875 Reorder the terms: -0.21875 + 0.21875 + 0.25x + x2 = 0 + 0.21875 Combine like terms: -0.21875 + 0.21875 = 0.00000 0.00000 + 0.25x + x2 = 0 + 0.21875 0.25x + x2 = 0 + 0.21875 Combine like terms: 0 + 0.21875 = 0.21875 0.25x + x2 = 0.21875 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = 0.21875 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 0.21875 + 0.015625 Combine like terms: 0.21875 + 0.015625 = 0.234375 0.015625 + 0.25x + x2 = 0.234375 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 0.234375 Calculate the square root of the right side: 0.484122918 Break this problem into two subproblems by setting (x + 0.125) equal to 0.484122918 and -0.484122918.Subproblem 1
x + 0.125 = 0.484122918 Simplifying x + 0.125 = 0.484122918 Reorder the terms: 0.125 + x = 0.484122918 Solving 0.125 + x = 0.484122918 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 0.484122918 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 0.484122918 + -0.125 x = 0.484122918 + -0.125 Combine like terms: 0.484122918 + -0.125 = 0.359122918 x = 0.359122918 Simplifying x = 0.359122918Subproblem 2
x + 0.125 = -0.484122918 Simplifying x + 0.125 = -0.484122918 Reorder the terms: 0.125 + x = -0.484122918 Solving 0.125 + x = -0.484122918 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -0.484122918 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -0.484122918 + -0.125 x = -0.484122918 + -0.125 Combine like terms: -0.484122918 + -0.125 = -0.609122918 x = -0.609122918 Simplifying x = -0.609122918Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.359122918, -0.609122918}Solution
x = {0.359122918, -0.609122918}
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