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Simplifying 0 = 78 + 15x + -4.9x2 Solving 0 = 78 + 15x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -78 = -78 -78 + -15x + 4.9x2 = 78 + 15x + -4.9x2 + -78 + -15x + 4.9x2 Reorder the terms: -78 + -15x + 4.9x2 = 78 + -78 + 15x + -15x + -4.9x2 + 4.9x2 Combine like terms: 78 + -78 = 0 -78 + -15x + 4.9x2 = 0 + 15x + -15x + -4.9x2 + 4.9x2 -78 + -15x + 4.9x2 = 15x + -15x + -4.9x2 + 4.9x2 Combine like terms: 15x + -15x = 0 -78 + -15x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -78 + -15x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -78 + -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'. -15.91836735 + -3.06122449x + x2 = 0 Move the constant term to the right: Add '15.91836735' to each side of the equation. -15.91836735 + -3.06122449x + 15.91836735 + x2 = 0 + 15.91836735 Reorder the terms: -15.91836735 + 15.91836735 + -3.06122449x + x2 = 0 + 15.91836735 Combine like terms: -15.91836735 + 15.91836735 = 0.00000000 0.00000000 + -3.06122449x + x2 = 0 + 15.91836735 -3.06122449x + x2 = 0 + 15.91836735 Combine like terms: 0 + 15.91836735 = 15.91836735 -3.06122449x + x2 = 15.91836735 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 = 15.91836735 + 2.342773845 Reorder the terms: 2.342773845 + -3.06122449x + x2 = 15.91836735 + 2.342773845 Combine like terms: 15.91836735 + 2.342773845 = 18.261141195 2.342773845 + -3.06122449x + x2 = 18.261141195 Factor a perfect square on the left side: (x + -1.530612245)(x + -1.530612245) = 18.261141195 Calculate the square root of the right side: 4.273305652 Break this problem into two subproblems by setting (x + -1.530612245) equal to 4.273305652 and -4.273305652.Subproblem 1
x + -1.530612245 = 4.273305652 Simplifying x + -1.530612245 = 4.273305652 Reorder the terms: -1.530612245 + x = 4.273305652 Solving -1.530612245 + x = 4.273305652 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 = 4.273305652 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + x = 4.273305652 + 1.530612245 x = 4.273305652 + 1.530612245 Combine like terms: 4.273305652 + 1.530612245 = 5.803917897 x = 5.803917897 Simplifying x = 5.803917897Subproblem 2
x + -1.530612245 = -4.273305652 Simplifying x + -1.530612245 = -4.273305652 Reorder the terms: -1.530612245 + x = -4.273305652 Solving -1.530612245 + x = -4.273305652 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 = -4.273305652 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + x = -4.273305652 + 1.530612245 x = -4.273305652 + 1.530612245 Combine like terms: -4.273305652 + 1.530612245 = -2.742693407 x = -2.742693407 Simplifying x = -2.742693407Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.803917897, -2.742693407}
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