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Simplifying 4x2 + 0.24x + -1(0.24)(4.5) = 0 Multiply -1 * 0.24 4x2 + 0.24x + -0.24 * 4.5 = 0 Multiply -0.24 * 4.5 4x2 + 0.24x + -1.08 = 0 Reorder the terms: -1.08 + 0.24x + 4x2 = 0 Solving -1.08 + 0.24x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.27 + 0.06x + x2 = 0 Move the constant term to the right: Add '0.27' to each side of the equation. -0.27 + 0.06x + 0.27 + x2 = 0 + 0.27 Reorder the terms: -0.27 + 0.27 + 0.06x + x2 = 0 + 0.27 Combine like terms: -0.27 + 0.27 = 0.00 0.00 + 0.06x + x2 = 0 + 0.27 0.06x + x2 = 0 + 0.27 Combine like terms: 0 + 0.27 = 0.27 0.06x + x2 = 0.27 The x term is 0.06x. Take half its coefficient (0.03). Square it (0.0009) and add it to both sides. Add '0.0009' to each side of the equation. 0.06x + 0.0009 + x2 = 0.27 + 0.0009 Reorder the terms: 0.0009 + 0.06x + x2 = 0.27 + 0.0009 Combine like terms: 0.27 + 0.0009 = 0.2709 0.0009 + 0.06x + x2 = 0.2709 Factor a perfect square on the left side: (x + 0.03)(x + 0.03) = 0.2709 Calculate the square root of the right side: 0.520480547 Break this problem into two subproblems by setting (x + 0.03) equal to 0.520480547 and -0.520480547.Subproblem 1
x + 0.03 = 0.520480547 Simplifying x + 0.03 = 0.520480547 Reorder the terms: 0.03 + x = 0.520480547 Solving 0.03 + x = 0.520480547 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03' to each side of the equation. 0.03 + -0.03 + x = 0.520480547 + -0.03 Combine like terms: 0.03 + -0.03 = 0.00 0.00 + x = 0.520480547 + -0.03 x = 0.520480547 + -0.03 Combine like terms: 0.520480547 + -0.03 = 0.490480547 x = 0.490480547 Simplifying x = 0.490480547Subproblem 2
x + 0.03 = -0.520480547 Simplifying x + 0.03 = -0.520480547 Reorder the terms: 0.03 + x = -0.520480547 Solving 0.03 + x = -0.520480547 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03' to each side of the equation. 0.03 + -0.03 + x = -0.520480547 + -0.03 Combine like terms: 0.03 + -0.03 = 0.00 0.00 + x = -0.520480547 + -0.03 x = -0.520480547 + -0.03 Combine like terms: -0.520480547 + -0.03 = -0.550480547 x = -0.550480547 Simplifying x = -0.550480547Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.490480547, -0.550480547}
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