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Simplifying 0.45x2 + 1.8x + -1.44 = 0 Reorder the terms: -1.44 + 1.8x + 0.45x2 = 0 Solving -1.44 + 1.8x + 0.45x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.45 the coefficient of the squared term: Divide each side by '0.45'. -3.2 + 4x + x2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + 4x + 3.2 + x2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + 4x + x2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + 4x + x2 = 0 + 3.2 4x + x2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 4x + x2 = 3.2 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 3.2 + 4 Reorder the terms: 4 + 4x + x2 = 3.2 + 4 Combine like terms: 3.2 + 4 = 7.2 4 + 4x + x2 = 7.2 Factor a perfect square on the left side: (x + 2)(x + 2) = 7.2 Calculate the square root of the right side: 2.683281573 Break this problem into two subproblems by setting (x + 2) equal to 2.683281573 and -2.683281573.Subproblem 1
x + 2 = 2.683281573 Simplifying x + 2 = 2.683281573 Reorder the terms: 2 + x = 2.683281573 Solving 2 + x = 2.683281573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.683281573 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.683281573 + -2 x = 2.683281573 + -2 Combine like terms: 2.683281573 + -2 = 0.683281573 x = 0.683281573 Simplifying x = 0.683281573Subproblem 2
x + 2 = -2.683281573 Simplifying x + 2 = -2.683281573 Reorder the terms: 2 + x = -2.683281573 Solving 2 + x = -2.683281573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.683281573 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.683281573 + -2 x = -2.683281573 + -2 Combine like terms: -2.683281573 + -2 = -4.683281573 x = -4.683281573 Simplifying x = -4.683281573Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.683281573, -4.683281573}
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