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Simplifying 2 = 15x + 4.9x2 Solving 2 = 15x + 4.9x2 Solving for variable 'x'. Reorder the terms: 2 + -15x + -4.9x2 = 15x + -15x + 4.9x2 + -4.9x2 Combine like terms: 15x + -15x = 0 2 + -15x + -4.9x2 = 0 + 4.9x2 + -4.9x2 2 + -15x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 2 + -15x + -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'. -0.4081632653 + 3.06122449x + x2 = 0 Move the constant term to the right: Add '0.4081632653' to each side of the equation. -0.4081632653 + 3.06122449x + 0.4081632653 + x2 = 0 + 0.4081632653 Reorder the terms: -0.4081632653 + 0.4081632653 + 3.06122449x + x2 = 0 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + 3.06122449x + x2 = 0 + 0.4081632653 3.06122449x + x2 = 0 + 0.4081632653 Combine like terms: 0 + 0.4081632653 = 0.4081632653 3.06122449x + x2 = 0.4081632653 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 = 0.4081632653 + 2.342773845 Reorder the terms: 2.342773845 + 3.06122449x + x2 = 0.4081632653 + 2.342773845 Combine like terms: 0.4081632653 + 2.342773845 = 2.7509371103 2.342773845 + 3.06122449x + x2 = 2.7509371103 Factor a perfect square on the left side: (x + 1.530612245)(x + 1.530612245) = 2.7509371103 Calculate the square root of the right side: 1.65859492 Break this problem into two subproblems by setting (x + 1.530612245) equal to 1.65859492 and -1.65859492.Subproblem 1
x + 1.530612245 = 1.65859492 Simplifying x + 1.530612245 = 1.65859492 Reorder the terms: 1.530612245 + x = 1.65859492 Solving 1.530612245 + x = 1.65859492 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 = 1.65859492 + -1.530612245 Combine like terms: 1.530612245 + -1.530612245 = 0.000000000 0.000000000 + x = 1.65859492 + -1.530612245 x = 1.65859492 + -1.530612245 Combine like terms: 1.65859492 + -1.530612245 = 0.127982675 x = 0.127982675 Simplifying x = 0.127982675Subproblem 2
x + 1.530612245 = -1.65859492 Simplifying x + 1.530612245 = -1.65859492 Reorder the terms: 1.530612245 + x = -1.65859492 Solving 1.530612245 + x = -1.65859492 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 = -1.65859492 + -1.530612245 Combine like terms: 1.530612245 + -1.530612245 = 0.000000000 0.000000000 + x = -1.65859492 + -1.530612245 x = -1.65859492 + -1.530612245 Combine like terms: -1.65859492 + -1.530612245 = -3.189207165 x = -3.189207165 Simplifying x = -3.189207165Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.127982675, -3.189207165}
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