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Simplifying -4.9x2 + 10x + 40 = 0 Reorder the terms: 40 + 10x + -4.9x2 = 0 Solving 40 + 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'. -8.163265306 + -2.040816327x + x2 = 0 Move the constant term to the right: Add '8.163265306' to each side of the equation. -8.163265306 + -2.040816327x + 8.163265306 + x2 = 0 + 8.163265306 Reorder the terms: -8.163265306 + 8.163265306 + -2.040816327x + x2 = 0 + 8.163265306 Combine like terms: -8.163265306 + 8.163265306 = 0.000000000 0.000000000 + -2.040816327x + x2 = 0 + 8.163265306 -2.040816327x + x2 = 0 + 8.163265306 Combine like terms: 0 + 8.163265306 = 8.163265306 -2.040816327x + x2 = 8.163265306 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 = 8.163265306 + 1.041232821 Reorder the terms: 1.041232821 + -2.040816327x + x2 = 8.163265306 + 1.041232821 Combine like terms: 8.163265306 + 1.041232821 = 9.204498127 1.041232821 + -2.040816327x + x2 = 9.204498127 Factor a perfect square on the left side: (x + -1.020408164)(x + -1.020408164) = 9.204498127 Calculate the square root of the right side: 3.033891581 Break this problem into two subproblems by setting (x + -1.020408164) equal to 3.033891581 and -3.033891581.Subproblem 1
x + -1.020408164 = 3.033891581 Simplifying x + -1.020408164 = 3.033891581 Reorder the terms: -1.020408164 + x = 3.033891581 Solving -1.020408164 + x = 3.033891581 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 = 3.033891581 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + x = 3.033891581 + 1.020408164 x = 3.033891581 + 1.020408164 Combine like terms: 3.033891581 + 1.020408164 = 4.054299745 x = 4.054299745 Simplifying x = 4.054299745Subproblem 2
x + -1.020408164 = -3.033891581 Simplifying x + -1.020408164 = -3.033891581 Reorder the terms: -1.020408164 + x = -3.033891581 Solving -1.020408164 + x = -3.033891581 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 = -3.033891581 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + x = -3.033891581 + 1.020408164 x = -3.033891581 + 1.020408164 Combine like terms: -3.033891581 + 1.020408164 = -2.013483417 x = -2.013483417 Simplifying x = -2.013483417Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.054299745, -2.013483417}
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