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Simplifying 0 = 150 + 10x + -4.9x2 Solving 0 = 150 + 10x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -150 = -150 -150 + -10x + 4.9x2 = 150 + 10x + -4.9x2 + -150 + -10x + 4.9x2 Reorder the terms: -150 + -10x + 4.9x2 = 150 + -150 + 10x + -10x + -4.9x2 + 4.9x2 Combine like terms: 150 + -150 = 0 -150 + -10x + 4.9x2 = 0 + 10x + -10x + -4.9x2 + 4.9x2 -150 + -10x + 4.9x2 = 10x + -10x + -4.9x2 + 4.9x2 Combine like terms: 10x + -10x = 0 -150 + -10x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -150 + -10x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -150 + -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'. -30.6122449 + -2.040816327x + x2 = 0 Move the constant term to the right: Add '30.6122449' to each side of the equation. -30.6122449 + -2.040816327x + 30.6122449 + x2 = 0 + 30.6122449 Reorder the terms: -30.6122449 + 30.6122449 + -2.040816327x + x2 = 0 + 30.6122449 Combine like terms: -30.6122449 + 30.6122449 = 0.0000000 0.0000000 + -2.040816327x + x2 = 0 + 30.6122449 -2.040816327x + x2 = 0 + 30.6122449 Combine like terms: 0 + 30.6122449 = 30.6122449 -2.040816327x + x2 = 30.6122449 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 = 30.6122449 + 1.041232821 Reorder the terms: 1.041232821 + -2.040816327x + x2 = 30.6122449 + 1.041232821 Combine like terms: 30.6122449 + 1.041232821 = 31.653477721 1.041232821 + -2.040816327x + x2 = 31.653477721 Factor a perfect square on the left side: (x + -1.020408164)(x + -1.020408164) = 31.653477721 Calculate the square root of the right side: 5.626142348 Break this problem into two subproblems by setting (x + -1.020408164) equal to 5.626142348 and -5.626142348.Subproblem 1
x + -1.020408164 = 5.626142348 Simplifying x + -1.020408164 = 5.626142348 Reorder the terms: -1.020408164 + x = 5.626142348 Solving -1.020408164 + x = 5.626142348 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 = 5.626142348 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + x = 5.626142348 + 1.020408164 x = 5.626142348 + 1.020408164 Combine like terms: 5.626142348 + 1.020408164 = 6.646550512 x = 6.646550512 Simplifying x = 6.646550512Subproblem 2
x + -1.020408164 = -5.626142348 Simplifying x + -1.020408164 = -5.626142348 Reorder the terms: -1.020408164 + x = -5.626142348 Solving -1.020408164 + x = -5.626142348 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 = -5.626142348 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + x = -5.626142348 + 1.020408164 x = -5.626142348 + 1.020408164 Combine like terms: -5.626142348 + 1.020408164 = -4.605734184 x = -4.605734184 Simplifying x = -4.605734184Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.646550512, -4.605734184}
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