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Simplifying -0.025x2 + 3.6x + 1.2 = 0 Reorder the terms: 1.2 + 3.6x + -0.025x2 = 0 Solving 1.2 + 3.6x + -0.025x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.025 the coefficient of the squared term: Divide each side by '-0.025'. -48 + -144x + x2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + -144x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + -144x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -144x + x2 = 0 + 48 -144x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 -144x + x2 = 48 The x term is -144x. Take half its coefficient (-72). Square it (5184) and add it to both sides. Add '5184' to each side of the equation. -144x + 5184 + x2 = 48 + 5184 Reorder the terms: 5184 + -144x + x2 = 48 + 5184 Combine like terms: 48 + 5184 = 5232 5184 + -144x + x2 = 5232 Factor a perfect square on the left side: (x + -72)(x + -72) = 5232 Calculate the square root of the right side: 72.33256528 Break this problem into two subproblems by setting (x + -72) equal to 72.33256528 and -72.33256528.Subproblem 1
x + -72 = 72.33256528 Simplifying x + -72 = 72.33256528 Reorder the terms: -72 + x = 72.33256528 Solving -72 + x = 72.33256528 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '72' to each side of the equation. -72 + 72 + x = 72.33256528 + 72 Combine like terms: -72 + 72 = 0 0 + x = 72.33256528 + 72 x = 72.33256528 + 72 Combine like terms: 72.33256528 + 72 = 144.33256528 x = 144.33256528 Simplifying x = 144.33256528Subproblem 2
x + -72 = -72.33256528 Simplifying x + -72 = -72.33256528 Reorder the terms: -72 + x = -72.33256528 Solving -72 + x = -72.33256528 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '72' to each side of the equation. -72 + 72 + x = -72.33256528 + 72 Combine like terms: -72 + 72 = 0 0 + x = -72.33256528 + 72 x = -72.33256528 + 72 Combine like terms: -72.33256528 + 72 = -0.33256528 x = -0.33256528 Simplifying x = -0.33256528Solution
The solution to the problem is based on the solutions from the subproblems. x = {144.33256528, -0.33256528}
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