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Simplifying x2(0.5) + 0.6x = 2 Reorder the terms for easier multiplication: 0.5x2 + 0.6x = 2 Reorder the terms: 0.6x + 0.5x2 = 2 Solving 0.6x + 0.5x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + 0.6x + 0.5x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 0.6x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -4 + 1.2x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 1.2x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 1.2x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 1.2x + x2 = 0 + 4 1.2x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 1.2x + x2 = 4 The x term is 1.2x. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x + 0.36 + x2 = 4 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 4 + 0.36 Combine like terms: 4 + 0.36 = 4.36 0.36 + 1.2x + x2 = 4.36 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 4.36 Calculate the square root of the right side: 2.088061302 Break this problem into two subproblems by setting (x + 0.6) equal to 2.088061302 and -2.088061302.Subproblem 1
x + 0.6 = 2.088061302 Simplifying x + 0.6 = 2.088061302 Reorder the terms: 0.6 + x = 2.088061302 Solving 0.6 + x = 2.088061302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 2.088061302 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 2.088061302 + -0.6 x = 2.088061302 + -0.6 Combine like terms: 2.088061302 + -0.6 = 1.488061302 x = 1.488061302 Simplifying x = 1.488061302Subproblem 2
x + 0.6 = -2.088061302 Simplifying x + 0.6 = -2.088061302 Reorder the terms: 0.6 + x = -2.088061302 Solving 0.6 + x = -2.088061302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -2.088061302 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -2.088061302 + -0.6 x = -2.088061302 + -0.6 Combine like terms: -2.088061302 + -0.6 = -2.688061302 x = -2.688061302 Simplifying x = -2.688061302Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.488061302, -2.688061302}
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