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Simplifying -45 = 10x + -4.9x2 Solving -45 = 10x + -4.9x2 Solving for variable 'x'. Reorder the terms: -45 + -10x + 4.9x2 = 10x + -10x + -4.9x2 + 4.9x2 Combine like terms: 10x + -10x = 0 -45 + -10x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -45 + -10x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -45 + -10x + 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'. -9.183673469 + -2.040816327x + x2 = 0 Move the constant term to the right: Add '9.183673469' to each side of the equation. -9.183673469 + -2.040816327x + 9.183673469 + x2 = 0 + 9.183673469 Reorder the terms: -9.183673469 + 9.183673469 + -2.040816327x + x2 = 0 + 9.183673469 Combine like terms: -9.183673469 + 9.183673469 = 0.000000000 0.000000000 + -2.040816327x + x2 = 0 + 9.183673469 -2.040816327x + x2 = 0 + 9.183673469 Combine like terms: 0 + 9.183673469 = 9.183673469 -2.040816327x + x2 = 9.183673469 The x term is -2.040816327x. Take half its coefficient (-1.020408164). Square it (1.041232821) and add it to both sides. Add '1.041232821' to each side of the equation. -2.040816327x + 1.041232821 + x2 = 9.183673469 + 1.041232821 Reorder the terms: 1.041232821 + -2.040816327x + x2 = 9.183673469 + 1.041232821 Combine like terms: 9.183673469 + 1.041232821 = 10.22490629 1.041232821 + -2.040816327x + x2 = 10.22490629 Factor a perfect square on the left side: (x + -1.020408164)(x + -1.020408164) = 10.22490629 Calculate the square root of the right side: 3.197640738 Break this problem into two subproblems by setting (x + -1.020408164) equal to 3.197640738 and -3.197640738.Subproblem 1
x + -1.020408164 = 3.197640738 Simplifying x + -1.020408164 = 3.197640738 Reorder the terms: -1.020408164 + x = 3.197640738 Solving -1.020408164 + x = 3.197640738 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.020408164' to each side of the equation. -1.020408164 + 1.020408164 + x = 3.197640738 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + x = 3.197640738 + 1.020408164 x = 3.197640738 + 1.020408164 Combine like terms: 3.197640738 + 1.020408164 = 4.218048902 x = 4.218048902 Simplifying x = 4.218048902Subproblem 2
x + -1.020408164 = -3.197640738 Simplifying x + -1.020408164 = -3.197640738 Reorder the terms: -1.020408164 + x = -3.197640738 Solving -1.020408164 + x = -3.197640738 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.020408164' to each side of the equation. -1.020408164 + 1.020408164 + x = -3.197640738 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + x = -3.197640738 + 1.020408164 x = -3.197640738 + 1.020408164 Combine like terms: -3.197640738 + 1.020408164 = -2.177232574 x = -2.177232574 Simplifying x = -2.177232574Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.218048902, -2.177232574}
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