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Simplifying 0 = -4.9x2 + -1.8x + 50 Reorder the terms: 0 = 50 + -1.8x + -4.9x2 Solving 0 = 50 + -1.8x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -50 = -50 -50 + 1.8x + 4.9x2 = 50 + -1.8x + -4.9x2 + -50 + 1.8x + 4.9x2 Reorder the terms: -50 + 1.8x + 4.9x2 = 50 + -50 + -1.8x + 1.8x + -4.9x2 + 4.9x2 Combine like terms: 50 + -50 = 0 -50 + 1.8x + 4.9x2 = 0 + -1.8x + 1.8x + -4.9x2 + 4.9x2 -50 + 1.8x + 4.9x2 = -1.8x + 1.8x + -4.9x2 + 4.9x2 Combine like terms: -1.8x + 1.8x = 0.0 -50 + 1.8x + 4.9x2 = 0.0 + -4.9x2 + 4.9x2 -50 + 1.8x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -50 + 1.8x + 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'. -10.20408163 + 0.3673469388x + x2 = 0 Move the constant term to the right: Add '10.20408163' to each side of the equation. -10.20408163 + 0.3673469388x + 10.20408163 + x2 = 0 + 10.20408163 Reorder the terms: -10.20408163 + 10.20408163 + 0.3673469388x + x2 = 0 + 10.20408163 Combine like terms: -10.20408163 + 10.20408163 = 0.00000000 0.00000000 + 0.3673469388x + x2 = 0 + 10.20408163 0.3673469388x + x2 = 0 + 10.20408163 Combine like terms: 0 + 10.20408163 = 10.20408163 0.3673469388x + x2 = 10.20408163 The x term is 0.3673469388x. Take half its coefficient (0.1836734694). Square it (0.03373594336) and add it to both sides. Add '0.03373594336' to each side of the equation. 0.3673469388x + 0.03373594336 + x2 = 10.20408163 + 0.03373594336 Reorder the terms: 0.03373594336 + 0.3673469388x + x2 = 10.20408163 + 0.03373594336 Combine like terms: 10.20408163 + 0.03373594336 = 10.23781757336 0.03373594336 + 0.3673469388x + x2 = 10.23781757336 Factor a perfect square on the left side: (x + 0.1836734694)(x + 0.1836734694) = 10.23781757336 Calculate the square root of the right side: 3.199658978 Break this problem into two subproblems by setting (x + 0.1836734694) equal to 3.199658978 and -3.199658978.Subproblem 1
x + 0.1836734694 = 3.199658978 Simplifying x + 0.1836734694 = 3.199658978 Reorder the terms: 0.1836734694 + x = 3.199658978 Solving 0.1836734694 + x = 3.199658978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1836734694' to each side of the equation. 0.1836734694 + -0.1836734694 + x = 3.199658978 + -0.1836734694 Combine like terms: 0.1836734694 + -0.1836734694 = 0.0000000000 0.0000000000 + x = 3.199658978 + -0.1836734694 x = 3.199658978 + -0.1836734694 Combine like terms: 3.199658978 + -0.1836734694 = 3.0159855086 x = 3.0159855086 Simplifying x = 3.0159855086Subproblem 2
x + 0.1836734694 = -3.199658978 Simplifying x + 0.1836734694 = -3.199658978 Reorder the terms: 0.1836734694 + x = -3.199658978 Solving 0.1836734694 + x = -3.199658978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1836734694' to each side of the equation. 0.1836734694 + -0.1836734694 + x = -3.199658978 + -0.1836734694 Combine like terms: 0.1836734694 + -0.1836734694 = 0.0000000000 0.0000000000 + x = -3.199658978 + -0.1836734694 x = -3.199658978 + -0.1836734694 Combine like terms: -3.199658978 + -0.1836734694 = -3.3833324474 x = -3.3833324474 Simplifying x = -3.3833324474Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.0159855086, -3.3833324474}
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