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Simplifying 15x + -4.9x2 = -30 Solving 15x + -4.9x2 = -30 Solving for variable 'x'. Reorder the terms: 30 + 15x + -4.9x2 = -30 + 30 Combine like terms: -30 + 30 = 0 30 + 15x + -4.9x2 = 0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -6.12244898 + -3.06122449x + x2 = 0 Move the constant term to the right: Add '6.12244898' to each side of the equation. -6.12244898 + -3.06122449x + 6.12244898 + x2 = 0 + 6.12244898 Reorder the terms: -6.12244898 + 6.12244898 + -3.06122449x + x2 = 0 + 6.12244898 Combine like terms: -6.12244898 + 6.12244898 = 0.00000000 0.00000000 + -3.06122449x + x2 = 0 + 6.12244898 -3.06122449x + x2 = 0 + 6.12244898 Combine like terms: 0 + 6.12244898 = 6.12244898 -3.06122449x + x2 = 6.12244898 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 = 6.12244898 + 2.342773845 Reorder the terms: 2.342773845 + -3.06122449x + x2 = 6.12244898 + 2.342773845 Combine like terms: 6.12244898 + 2.342773845 = 8.465222825 2.342773845 + -3.06122449x + x2 = 8.465222825 Factor a perfect square on the left side: (x + -1.530612245)(x + -1.530612245) = 8.465222825 Calculate the square root of the right side: 2.909505598 Break this problem into two subproblems by setting (x + -1.530612245) equal to 2.909505598 and -2.909505598.Subproblem 1
x + -1.530612245 = 2.909505598 Simplifying x + -1.530612245 = 2.909505598 Reorder the terms: -1.530612245 + x = 2.909505598 Solving -1.530612245 + x = 2.909505598 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 = 2.909505598 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + x = 2.909505598 + 1.530612245 x = 2.909505598 + 1.530612245 Combine like terms: 2.909505598 + 1.530612245 = 4.440117843 x = 4.440117843 Simplifying x = 4.440117843Subproblem 2
x + -1.530612245 = -2.909505598 Simplifying x + -1.530612245 = -2.909505598 Reorder the terms: -1.530612245 + x = -2.909505598 Solving -1.530612245 + x = -2.909505598 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 = -2.909505598 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + x = -2.909505598 + 1.530612245 x = -2.909505598 + 1.530612245 Combine like terms: -2.909505598 + 1.530612245 = -1.378893353 x = -1.378893353 Simplifying x = -1.378893353Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.440117843, -1.378893353}
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