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Simplifying 14.77066732x + 96.0743376 + -3.657463747x + -23.77351435 = 74.45x2 Reorder the terms: 96.0743376 + -23.77351435 + 14.77066732x + -3.657463747x = 74.45x2 Combine like terms: 96.0743376 + -23.77351435 = 72.30082325 72.30082325 + 14.77066732x + -3.657463747x = 74.45x2 Combine like terms: 14.77066732x + -3.657463747x = 11.113203573x 72.30082325 + 11.113203573x = 74.45x2 Solving 72.30082325 + 11.113203573x = 74.45x2 Solving for variable 'x'. Combine like terms: 74.45x2 + -74.45x2 = 0.00 72.30082325 + 11.113203573x + -74.45x2 = 0.00 Begin completing the square. Divide all terms by -74.45 the coefficient of the squared term: Divide each side by '-74.45'. -0.9711326158 + -0.1492706994x + x2 = 0 Move the constant term to the right: Add '0.9711326158' to each side of the equation. -0.9711326158 + -0.1492706994x + 0.9711326158 + x2 = 0 + 0.9711326158 Reorder the terms: -0.9711326158 + 0.9711326158 + -0.1492706994x + x2 = 0 + 0.9711326158 Combine like terms: -0.9711326158 + 0.9711326158 = 0.0000000000 0.0000000000 + -0.1492706994x + x2 = 0 + 0.9711326158 -0.1492706994x + x2 = 0 + 0.9711326158 Combine like terms: 0 + 0.9711326158 = 0.9711326158 -0.1492706994x + x2 = 0.9711326158 The x term is -0.1492706994x. Take half its coefficient (-0.0746353497). Square it (0.005570435425) and add it to both sides. Add '0.005570435425' to each side of the equation. -0.1492706994x + 0.005570435425 + x2 = 0.9711326158 + 0.005570435425 Reorder the terms: 0.005570435425 + -0.1492706994x + x2 = 0.9711326158 + 0.005570435425 Combine like terms: 0.9711326158 + 0.005570435425 = 0.976703051225 0.005570435425 + -0.1492706994x + x2 = 0.976703051225 Factor a perfect square on the left side: (x + -0.0746353497)(x + -0.0746353497) = 0.976703051225 Calculate the square root of the right side: 0.98828288 Break this problem into two subproblems by setting (x + -0.0746353497) equal to 0.98828288 and -0.98828288.Subproblem 1
x + -0.0746353497 = 0.98828288 Simplifying x + -0.0746353497 = 0.98828288 Reorder the terms: -0.0746353497 + x = 0.98828288 Solving -0.0746353497 + x = 0.98828288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0746353497' to each side of the equation. -0.0746353497 + 0.0746353497 + x = 0.98828288 + 0.0746353497 Combine like terms: -0.0746353497 + 0.0746353497 = 0.0000000000 0.0000000000 + x = 0.98828288 + 0.0746353497 x = 0.98828288 + 0.0746353497 Combine like terms: 0.98828288 + 0.0746353497 = 1.0629182297 x = 1.0629182297 Simplifying x = 1.0629182297Subproblem 2
x + -0.0746353497 = -0.98828288 Simplifying x + -0.0746353497 = -0.98828288 Reorder the terms: -0.0746353497 + x = -0.98828288 Solving -0.0746353497 + x = -0.98828288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0746353497' to each side of the equation. -0.0746353497 + 0.0746353497 + x = -0.98828288 + 0.0746353497 Combine like terms: -0.0746353497 + 0.0746353497 = 0.0000000000 0.0000000000 + x = -0.98828288 + 0.0746353497 x = -0.98828288 + 0.0746353497 Combine like terms: -0.98828288 + 0.0746353497 = -0.9136475303 x = -0.9136475303 Simplifying x = -0.9136475303Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0629182297, -0.9136475303}
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