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Simplifying 16x2 + -40x + 18 = 0 Reorder the terms: 18 + -40x + 16x2 = 0 Solving 18 + -40x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + -20x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + -20x + 8x2)' equal to zero and attempt to solve: Simplifying 9 + -20x + 8x2 = 0 Solving 9 + -20x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.125 + -2.5x + x2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + -2.5x + -1.125 + x2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + -2.5x + x2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + -2.5x + x2 = 0 + -1.125 -2.5x + x2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 -2.5x + x2 = -1.125 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 = -1.125 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -1.125 + 1.5625 Combine like terms: -1.125 + 1.5625 = 0.4375 1.5625 + -2.5x + x2 = 0.4375 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 0.4375 Calculate the square root of the right side: 0.661437828 Break this problem into two subproblems by setting (x + -1.25) equal to 0.661437828 and -0.661437828.Subproblem 1
x + -1.25 = 0.661437828 Simplifying x + -1.25 = 0.661437828 Reorder the terms: -1.25 + x = 0.661437828 Solving -1.25 + x = 0.661437828 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 = 0.661437828 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 0.661437828 + 1.25 x = 0.661437828 + 1.25 Combine like terms: 0.661437828 + 1.25 = 1.911437828 x = 1.911437828 Simplifying x = 1.911437828Subproblem 2
x + -1.25 = -0.661437828 Simplifying x + -1.25 = -0.661437828 Reorder the terms: -1.25 + x = -0.661437828 Solving -1.25 + x = -0.661437828 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 = -0.661437828 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -0.661437828 + 1.25 x = -0.661437828 + 1.25 Combine like terms: -0.661437828 + 1.25 = 0.588562172 x = 0.588562172 Simplifying x = 0.588562172Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.911437828, 0.588562172}Solution
x = {1.911437828, 0.588562172}
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