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Simplifying 16x2 + -60x + 8 = 0 Reorder the terms: 8 + -60x + 16x2 = 0 Solving 8 + -60x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(2 + -15x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + -15x + 4x2)' equal to zero and attempt to solve: Simplifying 2 + -15x + 4x2 = 0 Solving 2 + -15x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.5 + -3.75x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -3.75x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -3.75x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -3.75x + x2 = 0 + -0.5 -3.75x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -3.75x + x2 = -0.5 The x term is -3.75x. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75x + 3.515625 + x2 = -0.5 + 3.515625 Reorder the terms: 3.515625 + -3.75x + x2 = -0.5 + 3.515625 Combine like terms: -0.5 + 3.515625 = 3.015625 3.515625 + -3.75x + x2 = 3.015625 Factor a perfect square on the left side: (x + -1.875)(x + -1.875) = 3.015625 Calculate the square root of the right side: 1.736555499 Break this problem into two subproblems by setting (x + -1.875) equal to 1.736555499 and -1.736555499.Subproblem 1
x + -1.875 = 1.736555499 Simplifying x + -1.875 = 1.736555499 Reorder the terms: -1.875 + x = 1.736555499 Solving -1.875 + x = 1.736555499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = 1.736555499 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 1.736555499 + 1.875 x = 1.736555499 + 1.875 Combine like terms: 1.736555499 + 1.875 = 3.611555499 x = 3.611555499 Simplifying x = 3.611555499Subproblem 2
x + -1.875 = -1.736555499 Simplifying x + -1.875 = -1.736555499 Reorder the terms: -1.875 + x = -1.736555499 Solving -1.875 + x = -1.736555499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = -1.736555499 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = -1.736555499 + 1.875 x = -1.736555499 + 1.875 Combine like terms: -1.736555499 + 1.875 = 0.138444501 x = 0.138444501 Simplifying x = 0.138444501Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.611555499, 0.138444501}Solution
x = {3.611555499, 0.138444501}
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