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Simplifying 0 = -4.9x2 + 10x + 30 Reorder the terms: 0 = 30 + 10x + -4.9x2 Solving 0 = 30 + 10x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -30 = -30 -30 + -10x + 4.9x2 = 30 + 10x + -4.9x2 + -30 + -10x + 4.9x2 Reorder the terms: -30 + -10x + 4.9x2 = 30 + -30 + 10x + -10x + -4.9x2 + 4.9x2 Combine like terms: 30 + -30 = 0 -30 + -10x + 4.9x2 = 0 + 10x + -10x + -4.9x2 + 4.9x2 -30 + -10x + 4.9x2 = 10x + -10x + -4.9x2 + 4.9x2 Combine like terms: 10x + -10x = 0 -30 + -10x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -30 + -10x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -30 + -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'. -6.12244898 + -2.040816327x + x2 = 0 Move the constant term to the right: Add '6.12244898' to each side of the equation. -6.12244898 + -2.040816327x + 6.12244898 + x2 = 0 + 6.12244898 Reorder the terms: -6.12244898 + 6.12244898 + -2.040816327x + x2 = 0 + 6.12244898 Combine like terms: -6.12244898 + 6.12244898 = 0.00000000 0.00000000 + -2.040816327x + x2 = 0 + 6.12244898 -2.040816327x + x2 = 0 + 6.12244898 Combine like terms: 0 + 6.12244898 = 6.12244898 -2.040816327x + x2 = 6.12244898 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 = 6.12244898 + 1.041232821 Reorder the terms: 1.041232821 + -2.040816327x + x2 = 6.12244898 + 1.041232821 Combine like terms: 6.12244898 + 1.041232821 = 7.163681801 1.041232821 + -2.040816327x + x2 = 7.163681801 Factor a perfect square on the left side: (x + -1.020408164)(x + -1.020408164) = 7.163681801 Calculate the square root of the right side: 2.67650552 Break this problem into two subproblems by setting (x + -1.020408164) equal to 2.67650552 and -2.67650552.Subproblem 1
x + -1.020408164 = 2.67650552 Simplifying x + -1.020408164 = 2.67650552 Reorder the terms: -1.020408164 + x = 2.67650552 Solving -1.020408164 + x = 2.67650552 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 = 2.67650552 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + x = 2.67650552 + 1.020408164 x = 2.67650552 + 1.020408164 Combine like terms: 2.67650552 + 1.020408164 = 3.696913684 x = 3.696913684 Simplifying x = 3.696913684Subproblem 2
x + -1.020408164 = -2.67650552 Simplifying x + -1.020408164 = -2.67650552 Reorder the terms: -1.020408164 + x = -2.67650552 Solving -1.020408164 + x = -2.67650552 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 = -2.67650552 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + x = -2.67650552 + 1.020408164 x = -2.67650552 + 1.020408164 Combine like terms: -2.67650552 + 1.020408164 = -1.656097356 x = -1.656097356 Simplifying x = -1.656097356Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.696913684, -1.656097356}
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