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Simplifying 0.1x2 + 6x + -400 = 0 Reorder the terms: -400 + 6x + 0.1x2 = 0 Solving -400 + 6x + 0.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. -4000 + 60x + x2 = 0 Move the constant term to the right: Add '4000' to each side of the equation. -4000 + 60x + 4000 + x2 = 0 + 4000 Reorder the terms: -4000 + 4000 + 60x + x2 = 0 + 4000 Combine like terms: -4000 + 4000 = 0 0 + 60x + x2 = 0 + 4000 60x + x2 = 0 + 4000 Combine like terms: 0 + 4000 = 4000 60x + x2 = 4000 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 = 4000 + 900 Reorder the terms: 900 + 60x + x2 = 4000 + 900 Combine like terms: 4000 + 900 = 4900 900 + 60x + x2 = 4900 Factor a perfect square on the left side: (x + 30)(x + 30) = 4900 Calculate the square root of the right side: 70 Break this problem into two subproblems by setting (x + 30) equal to 70 and -70.Subproblem 1
x + 30 = 70 Simplifying x + 30 = 70 Reorder the terms: 30 + x = 70 Solving 30 + x = 70 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 = 70 + -30 Combine like terms: 30 + -30 = 0 0 + x = 70 + -30 x = 70 + -30 Combine like terms: 70 + -30 = 40 x = 40 Simplifying x = 40Subproblem 2
x + 30 = -70 Simplifying x + 30 = -70 Reorder the terms: 30 + x = -70 Solving 30 + x = -70 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 = -70 + -30 Combine like terms: 30 + -30 = 0 0 + x = -70 + -30 x = -70 + -30 Combine like terms: -70 + -30 = -100 x = -100 Simplifying x = -100Solution
The solution to the problem is based on the solutions from the subproblems. x = {40, -100}
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