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Simplifying 3x2 + -5x + 10 = 0.5x2 + 4x + 2 Reorder the terms: 10 + -5x + 3x2 = 0.5x2 + 4x + 2 Reorder the terms: 10 + -5x + 3x2 = 2 + 4x + 0.5x2 Solving 10 + -5x + 3x2 = 2 + 4x + 0.5x2 Solving for variable 'x'. Reorder the terms: 10 + -2 + -5x + -4x + 3x2 + -0.5x2 = 2 + 4x + 0.5x2 + -2 + -4x + -0.5x2 Combine like terms: 10 + -2 = 8 8 + -5x + -4x + 3x2 + -0.5x2 = 2 + 4x + 0.5x2 + -2 + -4x + -0.5x2 Combine like terms: -5x + -4x = -9x 8 + -9x + 3x2 + -0.5x2 = 2 + 4x + 0.5x2 + -2 + -4x + -0.5x2 Combine like terms: 3x2 + -0.5x2 = 2.5x2 8 + -9x + 2.5x2 = 2 + 4x + 0.5x2 + -2 + -4x + -0.5x2 Reorder the terms: 8 + -9x + 2.5x2 = 2 + -2 + 4x + -4x + 0.5x2 + -0.5x2 Combine like terms: 2 + -2 = 0 8 + -9x + 2.5x2 = 0 + 4x + -4x + 0.5x2 + -0.5x2 8 + -9x + 2.5x2 = 4x + -4x + 0.5x2 + -0.5x2 Combine like terms: 4x + -4x = 0 8 + -9x + 2.5x2 = 0 + 0.5x2 + -0.5x2 8 + -9x + 2.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 8 + -9x + 2.5x2 = 0.0 Begin completing the square. Divide all terms by 2.5 the coefficient of the squared term: Divide each side by '2.5'. 3.2 + -3.6x + x2 = 0 Move the constant term to the right: Add '-3.2' to each side of the equation. 3.2 + -3.6x + -3.2 + x2 = 0 + -3.2 Reorder the terms: 3.2 + -3.2 + -3.6x + x2 = 0 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + -3.6x + x2 = 0 + -3.2 -3.6x + x2 = 0 + -3.2 Combine like terms: 0 + -3.2 = -3.2 -3.6x + x2 = -3.2 The x term is -3.6x. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6x + 3.24 + x2 = -3.2 + 3.24 Reorder the terms: 3.24 + -3.6x + x2 = -3.2 + 3.24 Combine like terms: -3.2 + 3.24 = 0.04 3.24 + -3.6x + x2 = 0.04 Factor a perfect square on the left side: (x + -1.8)(x + -1.8) = 0.04 Calculate the square root of the right side: 0.2 Break this problem into two subproblems by setting (x + -1.8) equal to 0.2 and -0.2.Subproblem 1
x + -1.8 = 0.2 Simplifying x + -1.8 = 0.2 Reorder the terms: -1.8 + x = 0.2 Solving -1.8 + x = 0.2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = 0.2 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 0.2 + 1.8 x = 0.2 + 1.8 Combine like terms: 0.2 + 1.8 = 2 x = 2 Simplifying x = 2Subproblem 2
x + -1.8 = -0.2 Simplifying x + -1.8 = -0.2 Reorder the terms: -1.8 + x = -0.2 Solving -1.8 + x = -0.2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = -0.2 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -0.2 + 1.8 x = -0.2 + 1.8 Combine like terms: -0.2 + 1.8 = 1.6 x = 1.6 Simplifying x = 1.6Solution
The solution to the problem is based on the solutions from the subproblems. x = {2, 1.6}
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