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Simplifying 415 = 10x + 4.9x2 Solving 415 = 10x + 4.9x2 Solving for variable 'x'. Reorder the terms: 415 + -10x + -4.9x2 = 10x + -10x + 4.9x2 + -4.9x2 Combine like terms: 10x + -10x = 0 415 + -10x + -4.9x2 = 0 + 4.9x2 + -4.9x2 415 + -10x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 415 + -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'. -84.69387755 + 2.040816327x + x2 = 0 Move the constant term to the right: Add '84.69387755' to each side of the equation. -84.69387755 + 2.040816327x + 84.69387755 + x2 = 0 + 84.69387755 Reorder the terms: -84.69387755 + 84.69387755 + 2.040816327x + x2 = 0 + 84.69387755 Combine like terms: -84.69387755 + 84.69387755 = 0.00000000 0.00000000 + 2.040816327x + x2 = 0 + 84.69387755 2.040816327x + x2 = 0 + 84.69387755 Combine like terms: 0 + 84.69387755 = 84.69387755 2.040816327x + x2 = 84.69387755 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 = 84.69387755 + 1.041232821 Reorder the terms: 1.041232821 + 2.040816327x + x2 = 84.69387755 + 1.041232821 Combine like terms: 84.69387755 + 1.041232821 = 85.735110371 1.041232821 + 2.040816327x + x2 = 85.735110371 Factor a perfect square on the left side: (x + 1.020408164)(x + 1.020408164) = 85.735110371 Calculate the square root of the right side: 9.259325589 Break this problem into two subproblems by setting (x + 1.020408164) equal to 9.259325589 and -9.259325589.Subproblem 1
x + 1.020408164 = 9.259325589 Simplifying x + 1.020408164 = 9.259325589 Reorder the terms: 1.020408164 + x = 9.259325589 Solving 1.020408164 + x = 9.259325589 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 = 9.259325589 + -1.020408164 Combine like terms: 1.020408164 + -1.020408164 = 0.000000000 0.000000000 + x = 9.259325589 + -1.020408164 x = 9.259325589 + -1.020408164 Combine like terms: 9.259325589 + -1.020408164 = 8.238917425 x = 8.238917425 Simplifying x = 8.238917425Subproblem 2
x + 1.020408164 = -9.259325589 Simplifying x + 1.020408164 = -9.259325589 Reorder the terms: 1.020408164 + x = -9.259325589 Solving 1.020408164 + x = -9.259325589 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 = -9.259325589 + -1.020408164 Combine like terms: 1.020408164 + -1.020408164 = 0.000000000 0.000000000 + x = -9.259325589 + -1.020408164 x = -9.259325589 + -1.020408164 Combine like terms: -9.259325589 + -1.020408164 = -10.279733753 x = -10.279733753 Simplifying x = -10.279733753Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.238917425, -10.279733753}
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