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Simplifying 16x2 + 40x = 19 Reorder the terms: 40x + 16x2 = 19 Solving 40x + 16x2 = 19 Solving for variable 'x'. Reorder the terms: -19 + 40x + 16x2 = 19 + -19 Combine like terms: 19 + -19 = 0 -19 + 40x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.1875 + 2.5x + x2 = 0 Move the constant term to the right: Add '1.1875' to each side of the equation. -1.1875 + 2.5x + 1.1875 + x2 = 0 + 1.1875 Reorder the terms: -1.1875 + 1.1875 + 2.5x + x2 = 0 + 1.1875 Combine like terms: -1.1875 + 1.1875 = 0.0000 0.0000 + 2.5x + x2 = 0 + 1.1875 2.5x + x2 = 0 + 1.1875 Combine like terms: 0 + 1.1875 = 1.1875 2.5x + x2 = 1.1875 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 = 1.1875 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 1.1875 + 1.5625 Combine like terms: 1.1875 + 1.5625 = 2.75 1.5625 + 2.5x + x2 = 2.75 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (x + 1.25) equal to 1.658312395 and -1.658312395.Subproblem 1
x + 1.25 = 1.658312395 Simplifying x + 1.25 = 1.658312395 Reorder the terms: 1.25 + x = 1.658312395 Solving 1.25 + x = 1.658312395 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 = 1.658312395 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.658312395 + -1.25 x = 1.658312395 + -1.25 Combine like terms: 1.658312395 + -1.25 = 0.408312395 x = 0.408312395 Simplifying x = 0.408312395Subproblem 2
x + 1.25 = -1.658312395 Simplifying x + 1.25 = -1.658312395 Reorder the terms: 1.25 + x = -1.658312395 Solving 1.25 + x = -1.658312395 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 = -1.658312395 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.658312395 + -1.25 x = -1.658312395 + -1.25 Combine like terms: -1.658312395 + -1.25 = -2.908312395 x = -2.908312395 Simplifying x = -2.908312395Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.408312395, -2.908312395}
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