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Simplifying -16x2 + 40x + 202 = 0 Reorder the terms: 202 + 40x + -16x2 = 0 Solving 202 + 40x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(101 + 20x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(101 + 20x + -8x2)' equal to zero and attempt to solve: Simplifying 101 + 20x + -8x2 = 0 Solving 101 + 20x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -12.625 + -2.5x + x2 = 0 Move the constant term to the right: Add '12.625' to each side of the equation. -12.625 + -2.5x + 12.625 + x2 = 0 + 12.625 Reorder the terms: -12.625 + 12.625 + -2.5x + x2 = 0 + 12.625 Combine like terms: -12.625 + 12.625 = 0.000 0.000 + -2.5x + x2 = 0 + 12.625 -2.5x + x2 = 0 + 12.625 Combine like terms: 0 + 12.625 = 12.625 -2.5x + x2 = 12.625 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 = 12.625 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 12.625 + 1.5625 Combine like terms: 12.625 + 1.5625 = 14.1875 1.5625 + -2.5x + x2 = 14.1875 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 14.1875 Calculate the square root of the right side: 3.766629793 Break this problem into two subproblems by setting (x + -1.25) equal to 3.766629793 and -3.766629793.Subproblem 1
x + -1.25 = 3.766629793 Simplifying x + -1.25 = 3.766629793 Reorder the terms: -1.25 + x = 3.766629793 Solving -1.25 + x = 3.766629793 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 = 3.766629793 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 3.766629793 + 1.25 x = 3.766629793 + 1.25 Combine like terms: 3.766629793 + 1.25 = 5.016629793 x = 5.016629793 Simplifying x = 5.016629793Subproblem 2
x + -1.25 = -3.766629793 Simplifying x + -1.25 = -3.766629793 Reorder the terms: -1.25 + x = -3.766629793 Solving -1.25 + x = -3.766629793 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 = -3.766629793 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -3.766629793 + 1.25 x = -3.766629793 + 1.25 Combine like terms: -3.766629793 + 1.25 = -2.516629793 x = -2.516629793 Simplifying x = -2.516629793Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.016629793, -2.516629793}Solution
x = {5.016629793, -2.516629793}
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