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Simplifying 0 = 100 + 10x + -4.9x2 Solving 0 = 100 + 10x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -100 = -100 -100 + -10x + 4.9x2 = 100 + 10x + -4.9x2 + -100 + -10x + 4.9x2 Reorder the terms: -100 + -10x + 4.9x2 = 100 + -100 + 10x + -10x + -4.9x2 + 4.9x2 Combine like terms: 100 + -100 = 0 -100 + -10x + 4.9x2 = 0 + 10x + -10x + -4.9x2 + 4.9x2 -100 + -10x + 4.9x2 = 10x + -10x + -4.9x2 + 4.9x2 Combine like terms: 10x + -10x = 0 -100 + -10x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -100 + -10x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -100 + -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'. -20.40816327 + -2.040816327x + x2 = 0 Move the constant term to the right: Add '20.40816327' to each side of the equation. -20.40816327 + -2.040816327x + 20.40816327 + x2 = 0 + 20.40816327 Reorder the terms: -20.40816327 + 20.40816327 + -2.040816327x + x2 = 0 + 20.40816327 Combine like terms: -20.40816327 + 20.40816327 = 0.00000000 0.00000000 + -2.040816327x + x2 = 0 + 20.40816327 -2.040816327x + x2 = 0 + 20.40816327 Combine like terms: 0 + 20.40816327 = 20.40816327 -2.040816327x + x2 = 20.40816327 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 = 20.40816327 + 1.041232821 Reorder the terms: 1.041232821 + -2.040816327x + x2 = 20.40816327 + 1.041232821 Combine like terms: 20.40816327 + 1.041232821 = 21.449396091 1.041232821 + -2.040816327x + x2 = 21.449396091 Factor a perfect square on the left side: (x + -1.020408164)(x + -1.020408164) = 21.449396091 Calculate the square root of the right side: 4.631349273 Break this problem into two subproblems by setting (x + -1.020408164) equal to 4.631349273 and -4.631349273.Subproblem 1
x + -1.020408164 = 4.631349273 Simplifying x + -1.020408164 = 4.631349273 Reorder the terms: -1.020408164 + x = 4.631349273 Solving -1.020408164 + x = 4.631349273 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 = 4.631349273 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + x = 4.631349273 + 1.020408164 x = 4.631349273 + 1.020408164 Combine like terms: 4.631349273 + 1.020408164 = 5.651757437 x = 5.651757437 Simplifying x = 5.651757437Subproblem 2
x + -1.020408164 = -4.631349273 Simplifying x + -1.020408164 = -4.631349273 Reorder the terms: -1.020408164 + x = -4.631349273 Solving -1.020408164 + x = -4.631349273 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 = -4.631349273 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + x = -4.631349273 + 1.020408164 x = -4.631349273 + 1.020408164 Combine like terms: -4.631349273 + 1.020408164 = -3.610941109 x = -3.610941109 Simplifying x = -3.610941109Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.651757437, -3.610941109}
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