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Simplifying 4.9x2 + 15x + -50 = 0 Reorder the terms: -50 + 15x + 4.9x2 = 0 Solving -50 + 15x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -10.20408163 + 3.06122449x + x2 = 0 Move the constant term to the right: Add '10.20408163' to each side of the equation. -10.20408163 + 3.06122449x + 10.20408163 + x2 = 0 + 10.20408163 Reorder the terms: -10.20408163 + 10.20408163 + 3.06122449x + x2 = 0 + 10.20408163 Combine like terms: -10.20408163 + 10.20408163 = 0.00000000 0.00000000 + 3.06122449x + x2 = 0 + 10.20408163 3.06122449x + x2 = 0 + 10.20408163 Combine like terms: 0 + 10.20408163 = 10.20408163 3.06122449x + x2 = 10.20408163 The x term is 3.06122449x. Take half its coefficient (1.530612245). Square it (2.342773845) and add it to both sides. Add '2.342773845' to each side of the equation. 3.06122449x + 2.342773845 + x2 = 10.20408163 + 2.342773845 Reorder the terms: 2.342773845 + 3.06122449x + x2 = 10.20408163 + 2.342773845 Combine like terms: 10.20408163 + 2.342773845 = 12.546855475 2.342773845 + 3.06122449x + x2 = 12.546855475 Factor a perfect square on the left side: (x + 1.530612245)(x + 1.530612245) = 12.546855475 Calculate the square root of the right side: 3.542154073 Break this problem into two subproblems by setting (x + 1.530612245) equal to 3.542154073 and -3.542154073.Subproblem 1
x + 1.530612245 = 3.542154073 Simplifying x + 1.530612245 = 3.542154073 Reorder the terms: 1.530612245 + x = 3.542154073 Solving 1.530612245 + x = 3.542154073 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.530612245' to each side of the equation. 1.530612245 + -1.530612245 + x = 3.542154073 + -1.530612245 Combine like terms: 1.530612245 + -1.530612245 = 0.000000000 0.000000000 + x = 3.542154073 + -1.530612245 x = 3.542154073 + -1.530612245 Combine like terms: 3.542154073 + -1.530612245 = 2.011541828 x = 2.011541828 Simplifying x = 2.011541828Subproblem 2
x + 1.530612245 = -3.542154073 Simplifying x + 1.530612245 = -3.542154073 Reorder the terms: 1.530612245 + x = -3.542154073 Solving 1.530612245 + x = -3.542154073 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.530612245' to each side of the equation. 1.530612245 + -1.530612245 + x = -3.542154073 + -1.530612245 Combine like terms: 1.530612245 + -1.530612245 = 0.000000000 0.000000000 + x = -3.542154073 + -1.530612245 x = -3.542154073 + -1.530612245 Combine like terms: -3.542154073 + -1.530612245 = -5.072766318 x = -5.072766318 Simplifying x = -5.072766318Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.011541828, -5.072766318}
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