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Simplifying 3 + 80x + -16x2 = 6 Solving 3 + 80x + -16x2 = 6 Solving for variable 'x'. Reorder the terms: 3 + -6 + 80x + -16x2 = 6 + -6 Combine like terms: 3 + -6 = -3 -3 + 80x + -16x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -3 + 80x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 0.1875 + -5x + x2 = 0 Move the constant term to the right: Add '-0.1875' to each side of the equation. 0.1875 + -5x + -0.1875 + x2 = 0 + -0.1875 Reorder the terms: 0.1875 + -0.1875 + -5x + x2 = 0 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + -5x + x2 = 0 + -0.1875 -5x + x2 = 0 + -0.1875 Combine like terms: 0 + -0.1875 = -0.1875 -5x + x2 = -0.1875 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -0.1875 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -0.1875 + 6.25 Combine like terms: -0.1875 + 6.25 = 6.0625 6.25 + -5x + x2 = 6.0625 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (x + -2.5) equal to 2.46221445 and -2.46221445.Subproblem 1
x + -2.5 = 2.46221445 Simplifying x + -2.5 = 2.46221445 Reorder the terms: -2.5 + x = 2.46221445 Solving -2.5 + x = 2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.46221445 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.46221445 + 2.5 x = 2.46221445 + 2.5 Combine like terms: 2.46221445 + 2.5 = 4.96221445 x = 4.96221445 Simplifying x = 4.96221445Subproblem 2
x + -2.5 = -2.46221445 Simplifying x + -2.5 = -2.46221445 Reorder the terms: -2.5 + x = -2.46221445 Solving -2.5 + x = -2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.46221445 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.46221445 + 2.5 x = -2.46221445 + 2.5 Combine like terms: -2.46221445 + 2.5 = 0.03778555 x = 0.03778555 Simplifying x = 0.03778555Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.96221445, 0.03778555}
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