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Simplifying -0.01x2 + 0.6x + 5.8 = 0 Reorder the terms: 5.8 + 0.6x + -0.01x2 = 0 Solving 5.8 + 0.6x + -0.01x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. -580 + -60x + x2 = 0 Move the constant term to the right: Add '580' to each side of the equation. -580 + -60x + 580 + x2 = 0 + 580 Reorder the terms: -580 + 580 + -60x + x2 = 0 + 580 Combine like terms: -580 + 580 = 0 0 + -60x + x2 = 0 + 580 -60x + x2 = 0 + 580 Combine like terms: 0 + 580 = 580 -60x + x2 = 580 The x term is -60x. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60x + 900 + x2 = 580 + 900 Reorder the terms: 900 + -60x + x2 = 580 + 900 Combine like terms: 580 + 900 = 1480 900 + -60x + x2 = 1480 Factor a perfect square on the left side: (x + -30)(x + -30) = 1480 Calculate the square root of the right side: 38.470768123 Break this problem into two subproblems by setting (x + -30) equal to 38.470768123 and -38.470768123.Subproblem 1
x + -30 = 38.470768123 Simplifying x + -30 = 38.470768123 Reorder the terms: -30 + x = 38.470768123 Solving -30 + x = 38.470768123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 38.470768123 + 30 Combine like terms: -30 + 30 = 0 0 + x = 38.470768123 + 30 x = 38.470768123 + 30 Combine like terms: 38.470768123 + 30 = 68.470768123 x = 68.470768123 Simplifying x = 68.470768123Subproblem 2
x + -30 = -38.470768123 Simplifying x + -30 = -38.470768123 Reorder the terms: -30 + x = -38.470768123 Solving -30 + x = -38.470768123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = -38.470768123 + 30 Combine like terms: -30 + 30 = 0 0 + x = -38.470768123 + 30 x = -38.470768123 + 30 Combine like terms: -38.470768123 + 30 = -8.470768123 x = -8.470768123 Simplifying x = -8.470768123Solution
The solution to the problem is based on the solutions from the subproblems. x = {68.470768123, -8.470768123}
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