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Simplifying 4.25 = (0.5)(9.8)(x2) + 4.636x Multiply 0.5 * 9.8 4.25 = 4.9x2 + 4.636x Reorder the terms: 4.25 = 4.636x + 4.9x2 Solving 4.25 = 4.636x + 4.9x2 Solving for variable 'x'. Reorder the terms: 4.25 + -4.636x + -4.9x2 = 4.636x + -4.636x + 4.9x2 + -4.9x2 Combine like terms: 4.636x + -4.636x = 0.000 4.25 + -4.636x + -4.9x2 = 0.000 + 4.9x2 + -4.9x2 4.25 + -4.636x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 4.25 + -4.636x + -4.9x2 = 0.0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -0.8673469388 + 0.946122449x + x2 = 0 Move the constant term to the right: Add '0.8673469388' to each side of the equation. -0.8673469388 + 0.946122449x + 0.8673469388 + x2 = 0 + 0.8673469388 Reorder the terms: -0.8673469388 + 0.8673469388 + 0.946122449x + x2 = 0 + 0.8673469388 Combine like terms: -0.8673469388 + 0.8673469388 = 0.0000000000 0.0000000000 + 0.946122449x + x2 = 0 + 0.8673469388 0.946122449x + x2 = 0 + 0.8673469388 Combine like terms: 0 + 0.8673469388 = 0.8673469388 0.946122449x + x2 = 0.8673469388 The x term is 0.946122449x. Take half its coefficient (0.4730612245). Square it (0.2237869221) and add it to both sides. Add '0.2237869221' to each side of the equation. 0.946122449x + 0.2237869221 + x2 = 0.8673469388 + 0.2237869221 Reorder the terms: 0.2237869221 + 0.946122449x + x2 = 0.8673469388 + 0.2237869221 Combine like terms: 0.8673469388 + 0.2237869221 = 1.0911338609 0.2237869221 + 0.946122449x + x2 = 1.0911338609 Factor a perfect square on the left side: (x + 0.4730612245)(x + 0.4730612245) = 1.0911338609 Calculate the square root of the right side: 1.044573531 Break this problem into two subproblems by setting (x + 0.4730612245) equal to 1.044573531 and -1.044573531.Subproblem 1
x + 0.4730612245 = 1.044573531 Simplifying x + 0.4730612245 = 1.044573531 Reorder the terms: 0.4730612245 + x = 1.044573531 Solving 0.4730612245 + x = 1.044573531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4730612245' to each side of the equation. 0.4730612245 + -0.4730612245 + x = 1.044573531 + -0.4730612245 Combine like terms: 0.4730612245 + -0.4730612245 = 0.0000000000 0.0000000000 + x = 1.044573531 + -0.4730612245 x = 1.044573531 + -0.4730612245 Combine like terms: 1.044573531 + -0.4730612245 = 0.5715123065 x = 0.5715123065 Simplifying x = 0.5715123065Subproblem 2
x + 0.4730612245 = -1.044573531 Simplifying x + 0.4730612245 = -1.044573531 Reorder the terms: 0.4730612245 + x = -1.044573531 Solving 0.4730612245 + x = -1.044573531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4730612245' to each side of the equation. 0.4730612245 + -0.4730612245 + x = -1.044573531 + -0.4730612245 Combine like terms: 0.4730612245 + -0.4730612245 = 0.0000000000 0.0000000000 + x = -1.044573531 + -0.4730612245 x = -1.044573531 + -0.4730612245 Combine like terms: -1.044573531 + -0.4730612245 = -1.5176347555 x = -1.5176347555 Simplifying x = -1.5176347555Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5715123065, -1.5176347555}
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