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Simplifying 4.9x2 + -15x + -51 = 0 Reorder the terms: -51 + -15x + 4.9x2 = 0 Solving -51 + -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'. -10.40816327 + -3.06122449x + x2 = 0 Move the constant term to the right: Add '10.40816327' to each side of the equation. -10.40816327 + -3.06122449x + 10.40816327 + x2 = 0 + 10.40816327 Reorder the terms: -10.40816327 + 10.40816327 + -3.06122449x + x2 = 0 + 10.40816327 Combine like terms: -10.40816327 + 10.40816327 = 0.00000000 0.00000000 + -3.06122449x + x2 = 0 + 10.40816327 -3.06122449x + x2 = 0 + 10.40816327 Combine like terms: 0 + 10.40816327 = 10.40816327 -3.06122449x + x2 = 10.40816327 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 = 10.40816327 + 2.342773845 Reorder the terms: 2.342773845 + -3.06122449x + x2 = 10.40816327 + 2.342773845 Combine like terms: 10.40816327 + 2.342773845 = 12.750937115 2.342773845 + -3.06122449x + x2 = 12.750937115 Factor a perfect square on the left side: (x + -1.530612245)(x + -1.530612245) = 12.750937115 Calculate the square root of the right side: 3.570845434 Break this problem into two subproblems by setting (x + -1.530612245) equal to 3.570845434 and -3.570845434.Subproblem 1
x + -1.530612245 = 3.570845434 Simplifying x + -1.530612245 = 3.570845434 Reorder the terms: -1.530612245 + x = 3.570845434 Solving -1.530612245 + x = 3.570845434 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 = 3.570845434 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + x = 3.570845434 + 1.530612245 x = 3.570845434 + 1.530612245 Combine like terms: 3.570845434 + 1.530612245 = 5.101457679 x = 5.101457679 Simplifying x = 5.101457679Subproblem 2
x + -1.530612245 = -3.570845434 Simplifying x + -1.530612245 = -3.570845434 Reorder the terms: -1.530612245 + x = -3.570845434 Solving -1.530612245 + x = -3.570845434 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 = -3.570845434 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + x = -3.570845434 + 1.530612245 x = -3.570845434 + 1.530612245 Combine like terms: -3.570845434 + 1.530612245 = -2.040233189 x = -2.040233189 Simplifying x = -2.040233189Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.101457679, -2.040233189}
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