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Simplifying 4.9x2 + 10x + -60 = 0 Reorder the terms: -60 + 10x + 4.9x2 = 0 Solving -60 + 10x + 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'. -12.24489796 + 2.040816327x + x2 = 0 Move the constant term to the right: Add '12.24489796' to each side of the equation. -12.24489796 + 2.040816327x + 12.24489796 + x2 = 0 + 12.24489796 Reorder the terms: -12.24489796 + 12.24489796 + 2.040816327x + x2 = 0 + 12.24489796 Combine like terms: -12.24489796 + 12.24489796 = 0.00000000 0.00000000 + 2.040816327x + x2 = 0 + 12.24489796 2.040816327x + x2 = 0 + 12.24489796 Combine like terms: 0 + 12.24489796 = 12.24489796 2.040816327x + x2 = 12.24489796 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 = 12.24489796 + 1.041232821 Reorder the terms: 1.041232821 + 2.040816327x + x2 = 12.24489796 + 1.041232821 Combine like terms: 12.24489796 + 1.041232821 = 13.286130781 1.041232821 + 2.040816327x + x2 = 13.286130781 Factor a perfect square on the left side: (x + 1.020408164)(x + 1.020408164) = 13.286130781 Calculate the square root of the right side: 3.64501451 Break this problem into two subproblems by setting (x + 1.020408164) equal to 3.64501451 and -3.64501451.Subproblem 1
x + 1.020408164 = 3.64501451 Simplifying x + 1.020408164 = 3.64501451 Reorder the terms: 1.020408164 + x = 3.64501451 Solving 1.020408164 + x = 3.64501451 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 = 3.64501451 + -1.020408164 Combine like terms: 1.020408164 + -1.020408164 = 0.000000000 0.000000000 + x = 3.64501451 + -1.020408164 x = 3.64501451 + -1.020408164 Combine like terms: 3.64501451 + -1.020408164 = 2.624606346 x = 2.624606346 Simplifying x = 2.624606346Subproblem 2
x + 1.020408164 = -3.64501451 Simplifying x + 1.020408164 = -3.64501451 Reorder the terms: 1.020408164 + x = -3.64501451 Solving 1.020408164 + x = -3.64501451 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 = -3.64501451 + -1.020408164 Combine like terms: 1.020408164 + -1.020408164 = 0.000000000 0.000000000 + x = -3.64501451 + -1.020408164 x = -3.64501451 + -1.020408164 Combine like terms: -3.64501451 + -1.020408164 = -4.665422674 x = -4.665422674 Simplifying x = -4.665422674Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.624606346, -4.665422674}
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