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Simplifying -4.9x2 + -1x + 75 = 0 Reorder the terms: 75 + -1x + -4.9x2 = 0 Solving 75 + -1x + -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'. -15.30612245 + 0.2040816327x + x2 = 0 Move the constant term to the right: Add '15.30612245' to each side of the equation. -15.30612245 + 0.2040816327x + 15.30612245 + x2 = 0 + 15.30612245 Reorder the terms: -15.30612245 + 15.30612245 + 0.2040816327x + x2 = 0 + 15.30612245 Combine like terms: -15.30612245 + 15.30612245 = 0.00000000 0.00000000 + 0.2040816327x + x2 = 0 + 15.30612245 0.2040816327x + x2 = 0 + 15.30612245 Combine like terms: 0 + 15.30612245 = 15.30612245 0.2040816327x + x2 = 15.30612245 The x term is 0.2040816327x. Take half its coefficient (0.1020408164). Square it (0.01041232821) and add it to both sides. Add '0.01041232821' to each side of the equation. 0.2040816327x + 0.01041232821 + x2 = 15.30612245 + 0.01041232821 Reorder the terms: 0.01041232821 + 0.2040816327x + x2 = 15.30612245 + 0.01041232821 Combine like terms: 15.30612245 + 0.01041232821 = 15.31653477821 0.01041232821 + 0.2040816327x + x2 = 15.31653477821 Factor a perfect square on the left side: (x + 0.1020408164)(x + 0.1020408164) = 15.31653477821 Calculate the square root of the right side: 3.913634472 Break this problem into two subproblems by setting (x + 0.1020408164) equal to 3.913634472 and -3.913634472.Subproblem 1
x + 0.1020408164 = 3.913634472 Simplifying x + 0.1020408164 = 3.913634472 Reorder the terms: 0.1020408164 + x = 3.913634472 Solving 0.1020408164 + x = 3.913634472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1020408164' to each side of the equation. 0.1020408164 + -0.1020408164 + x = 3.913634472 + -0.1020408164 Combine like terms: 0.1020408164 + -0.1020408164 = 0.0000000000 0.0000000000 + x = 3.913634472 + -0.1020408164 x = 3.913634472 + -0.1020408164 Combine like terms: 3.913634472 + -0.1020408164 = 3.8115936556 x = 3.8115936556 Simplifying x = 3.8115936556Subproblem 2
x + 0.1020408164 = -3.913634472 Simplifying x + 0.1020408164 = -3.913634472 Reorder the terms: 0.1020408164 + x = -3.913634472 Solving 0.1020408164 + x = -3.913634472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1020408164' to each side of the equation. 0.1020408164 + -0.1020408164 + x = -3.913634472 + -0.1020408164 Combine like terms: 0.1020408164 + -0.1020408164 = 0.0000000000 0.0000000000 + x = -3.913634472 + -0.1020408164 x = -3.913634472 + -0.1020408164 Combine like terms: -3.913634472 + -0.1020408164 = -4.0156752884 x = -4.0156752884 Simplifying x = -4.0156752884Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.8115936556, -4.0156752884}
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