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Simplifying 1.8(x2 + -3x + 2) = x2 Reorder the terms: 1.8(2 + -3x + x2) = x2 (2 * 1.8 + -3x * 1.8 + x2 * 1.8) = x2 (3.6 + -5.4x + 1.8x2) = x2 Solving 3.6 + -5.4x + 1.8x2 = x2 Solving for variable 'x'. Combine like terms: 1.8x2 + -1x2 = 0.8x2 3.6 + -5.4x + 0.8x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 3.6 + -5.4x + 0.8x2 = 0 Begin completing the square. Divide all terms by 0.8 the coefficient of the squared term: Divide each side by '0.8'. 4.5 + -6.75x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + -6.75x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + -6.75x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -6.75x + x2 = 0 + -4.5 -6.75x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 -6.75x + x2 = -4.5 The x term is -6.75x. Take half its coefficient (-3.375). Square it (11.390625) and add it to both sides. Add '11.390625' to each side of the equation. -6.75x + 11.390625 + x2 = -4.5 + 11.390625 Reorder the terms: 11.390625 + -6.75x + x2 = -4.5 + 11.390625 Combine like terms: -4.5 + 11.390625 = 6.890625 11.390625 + -6.75x + x2 = 6.890625 Factor a perfect square on the left side: (x + -3.375)(x + -3.375) = 6.890625 Calculate the square root of the right side: 2.625 Break this problem into two subproblems by setting (x + -3.375) equal to 2.625 and -2.625.Subproblem 1
x + -3.375 = 2.625 Simplifying x + -3.375 = 2.625 Reorder the terms: -3.375 + x = 2.625 Solving -3.375 + x = 2.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = 2.625 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = 2.625 + 3.375 x = 2.625 + 3.375 Combine like terms: 2.625 + 3.375 = 6 x = 6 Simplifying x = 6Subproblem 2
x + -3.375 = -2.625 Simplifying x + -3.375 = -2.625 Reorder the terms: -3.375 + x = -2.625 Solving -3.375 + x = -2.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = -2.625 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = -2.625 + 3.375 x = -2.625 + 3.375 Combine like terms: -2.625 + 3.375 = 0.75 x = 0.75 Simplifying x = 0.75Solution
The solution to the problem is based on the solutions from the subproblems. x = {6, 0.75}
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