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Simplifying 50 = 1.7x + 5.0x2 Solving 50 = 1.7x + 5.0x2 Solving for variable 'x'. Reorder the terms: 50 + -1.7x + -5.0x2 = 1.7x + -1.7x + 5.0x2 + -5.0x2 Combine like terms: 1.7x + -1.7x = 0.0 50 + -1.7x + -5.0x2 = 0.0 + 5.0x2 + -5.0x2 50 + -1.7x + -5.0x2 = 5.0x2 + -5.0x2 Combine like terms: 5.0x2 + -5.0x2 = 0.0 50 + -1.7x + -5.0x2 = 0.0 Begin completing the square. Divide all terms by -5.0 the coefficient of the squared term: Divide each side by '-5.0'. -10 + 0.34x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 0.34x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 0.34x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 0.34x + x2 = 0 + 10 0.34x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 0.34x + x2 = 10 The x term is 0.34x. Take half its coefficient (0.17). Square it (0.0289) and add it to both sides. Add '0.0289' to each side of the equation. 0.34x + 0.0289 + x2 = 10 + 0.0289 Reorder the terms: 0.0289 + 0.34x + x2 = 10 + 0.0289 Combine like terms: 10 + 0.0289 = 10.0289 0.0289 + 0.34x + x2 = 10.0289 Factor a perfect square on the left side: (x + 0.17)(x + 0.17) = 10.0289 Calculate the square root of the right side: 3.166843855 Break this problem into two subproblems by setting (x + 0.17) equal to 3.166843855 and -3.166843855.Subproblem 1
x + 0.17 = 3.166843855 Simplifying x + 0.17 = 3.166843855 Reorder the terms: 0.17 + x = 3.166843855 Solving 0.17 + x = 3.166843855 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.17' to each side of the equation. 0.17 + -0.17 + x = 3.166843855 + -0.17 Combine like terms: 0.17 + -0.17 = 0.00 0.00 + x = 3.166843855 + -0.17 x = 3.166843855 + -0.17 Combine like terms: 3.166843855 + -0.17 = 2.996843855 x = 2.996843855 Simplifying x = 2.996843855Subproblem 2
x + 0.17 = -3.166843855 Simplifying x + 0.17 = -3.166843855 Reorder the terms: 0.17 + x = -3.166843855 Solving 0.17 + x = -3.166843855 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.17' to each side of the equation. 0.17 + -0.17 + x = -3.166843855 + -0.17 Combine like terms: 0.17 + -0.17 = 0.00 0.00 + x = -3.166843855 + -0.17 x = -3.166843855 + -0.17 Combine like terms: -3.166843855 + -0.17 = -3.336843855 x = -3.336843855 Simplifying x = -3.336843855Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.996843855, -3.336843855}
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