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Simplifying 16x2 + -40x + 10 = 0 Reorder the terms: 10 + -40x + 16x2 = 0 Solving 10 + -40x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -20x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -20x + 8x2)' equal to zero and attempt to solve: Simplifying 5 + -20x + 8x2 = 0 Solving 5 + -20x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.625 + -2.5x + x2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + -2.5x + -0.625 + x2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + -2.5x + x2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + -2.5x + x2 = 0 + -0.625 -2.5x + x2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 -2.5x + x2 = -0.625 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = -0.625 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -0.625 + 1.5625 Combine like terms: -0.625 + 1.5625 = 0.9375 1.5625 + -2.5x + x2 = 0.9375 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 0.9375 Calculate the square root of the right side: 0.968245837 Break this problem into two subproblems by setting (x + -1.25) equal to 0.968245837 and -0.968245837.Subproblem 1
x + -1.25 = 0.968245837 Simplifying x + -1.25 = 0.968245837 Reorder the terms: -1.25 + x = 0.968245837 Solving -1.25 + x = 0.968245837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 0.968245837 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 0.968245837 + 1.25 x = 0.968245837 + 1.25 Combine like terms: 0.968245837 + 1.25 = 2.218245837 x = 2.218245837 Simplifying x = 2.218245837Subproblem 2
x + -1.25 = -0.968245837 Simplifying x + -1.25 = -0.968245837 Reorder the terms: -1.25 + x = -0.968245837 Solving -1.25 + x = -0.968245837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -0.968245837 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -0.968245837 + 1.25 x = -0.968245837 + 1.25 Combine like terms: -0.968245837 + 1.25 = 0.281754163 x = 0.281754163 Simplifying x = 0.281754163Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.218245837, 0.281754163}Solution
x = {2.218245837, 0.281754163}
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