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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 = 2.177232574 x = 2.177232574 Simplifying x = 2.177232574Subproblem 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 = -4.218048902 x = -4.218048902 Simplifying x = -4.218048902Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.177232574, -4.218048902}
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