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Simplifying 0.1x2 + 2.4x + -180 = 0 Reorder the terms: -180 + 2.4x + 0.1x2 = 0 Solving -180 + 2.4x + 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'. -1800 + 24x + x2 = 0 Move the constant term to the right: Add '1800' to each side of the equation. -1800 + 24x + 1800 + x2 = 0 + 1800 Reorder the terms: -1800 + 1800 + 24x + x2 = 0 + 1800 Combine like terms: -1800 + 1800 = 0 0 + 24x + x2 = 0 + 1800 24x + x2 = 0 + 1800 Combine like terms: 0 + 1800 = 1800 24x + x2 = 1800 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = 1800 + 144 Reorder the terms: 144 + 24x + x2 = 1800 + 144 Combine like terms: 1800 + 144 = 1944 144 + 24x + x2 = 1944 Factor a perfect square on the left side: (x + 12)(x + 12) = 1944 Calculate the square root of the right side: 44.09081537 Break this problem into two subproblems by setting (x + 12) equal to 44.09081537 and -44.09081537.Subproblem 1
x + 12 = 44.09081537 Simplifying x + 12 = 44.09081537 Reorder the terms: 12 + x = 44.09081537 Solving 12 + x = 44.09081537 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 44.09081537 + -12 Combine like terms: 12 + -12 = 0 0 + x = 44.09081537 + -12 x = 44.09081537 + -12 Combine like terms: 44.09081537 + -12 = 32.09081537 x = 32.09081537 Simplifying x = 32.09081537Subproblem 2
x + 12 = -44.09081537 Simplifying x + 12 = -44.09081537 Reorder the terms: 12 + x = -44.09081537 Solving 12 + x = -44.09081537 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -44.09081537 + -12 Combine like terms: 12 + -12 = 0 0 + x = -44.09081537 + -12 x = -44.09081537 + -12 Combine like terms: -44.09081537 + -12 = -56.09081537 x = -56.09081537 Simplifying x = -56.09081537Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.09081537, -56.09081537}
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