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Simplifying (-16x2) + (22x) + 310 = 0 Reorder the terms: 310 + (22x) + (-16x2) = 0 Solving 310 + (22x) + (-16x2) = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(155 + (11x) + (-8x2)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(155 + (11x) + (-8x2))' equal to zero and attempt to solve: Simplifying 155 + (11x) + (-8x2) = 0 Solving 155 + (11x) + (-8x2) = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -19.375 + (-1.375x) + x2 = 0 Move the constant term to the right: Add '19.375' to each side of the equation. -19.375 + (-1.375x) + 19.375 + x2 = 0 + 19.375 Reorder the terms: -19.375 + 19.375 + (-1.375x) + x2 = 0 + 19.375 Combine like terms: -19.375 + 19.375 = 0.000 0.000 + (-1.375x) + x2 = 0 + 19.375 (-1.375x) + x2 = 0 + 19.375 Combine like terms: 0 + 19.375 = 19.375 (-1.375x) + x2 = 19.375 The x term is (-1.375x). Take half its coefficient (-0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. (-1.375x) + 0.47265625 + x2 = 19.375 + 0.47265625 Reorder the terms: 0.47265625 + (-1.375x) + x2 = 19.375 + 0.47265625 Combine like terms: 19.375 + 0.47265625 = 19.84765625 0.47265625 + (-1.375x) + x2 = 19.84765625 Factor a perfect square on the left side: ((x) + -0.6875)((x) + -0.6875) = 19.84765625 Calculate the square root of the right side: 4.455070847 Break this problem into two subproblems by setting ((x) + -0.6875) equal to 4.455070847 and -4.455070847.Subproblem 1
(x) + -0.6875 = 4.455070847 Simplifying (x) + -0.6875 = 4.455070847 x + -0.6875 = 4.455070847 Reorder the terms: -0.6875 + x = 4.455070847 Solving -0.6875 + x = 4.455070847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + x = 4.455070847 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + x = 4.455070847 + 0.6875 x = 4.455070847 + 0.6875 Combine like terms: 4.455070847 + 0.6875 = 5.142570847 x = 5.142570847 Simplifying x = 5.142570847Subproblem 2
(x) + -0.6875 = -4.455070847 Simplifying (x) + -0.6875 = -4.455070847 x + -0.6875 = -4.455070847 Reorder the terms: -0.6875 + x = -4.455070847 Solving -0.6875 + x = -4.455070847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + x = -4.455070847 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + x = -4.455070847 + 0.6875 x = -4.455070847 + 0.6875 Combine like terms: -4.455070847 + 0.6875 = -3.767570847 x = -3.767570847 Simplifying x = -3.767570847Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.142570847, -3.767570847}Solution
x = {5.142570847, -3.767570847}
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