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Simplifying 4x2 + 1.52x + -1.064 = 0 Reorder the terms: -1.064 + 1.52x + 4x2 = 0 Solving -1.064 + 1.52x + 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'. -0.266 + 0.38x + x2 = 0 Move the constant term to the right: Add '0.266' to each side of the equation. -0.266 + 0.38x + 0.266 + x2 = 0 + 0.266 Reorder the terms: -0.266 + 0.266 + 0.38x + x2 = 0 + 0.266 Combine like terms: -0.266 + 0.266 = 0.000 0.000 + 0.38x + x2 = 0 + 0.266 0.38x + x2 = 0 + 0.266 Combine like terms: 0 + 0.266 = 0.266 0.38x + x2 = 0.266 The x term is 0.38x. Take half its coefficient (0.19). Square it (0.0361) and add it to both sides. Add '0.0361' to each side of the equation. 0.38x + 0.0361 + x2 = 0.266 + 0.0361 Reorder the terms: 0.0361 + 0.38x + x2 = 0.266 + 0.0361 Combine like terms: 0.266 + 0.0361 = 0.3021 0.0361 + 0.38x + x2 = 0.3021 Factor a perfect square on the left side: (x + 0.19)(x + 0.19) = 0.3021 Calculate the square root of the right side: 0.549636243 Break this problem into two subproblems by setting (x + 0.19) equal to 0.549636243 and -0.549636243.Subproblem 1
x + 0.19 = 0.549636243 Simplifying x + 0.19 = 0.549636243 Reorder the terms: 0.19 + x = 0.549636243 Solving 0.19 + x = 0.549636243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.19' to each side of the equation. 0.19 + -0.19 + x = 0.549636243 + -0.19 Combine like terms: 0.19 + -0.19 = 0.00 0.00 + x = 0.549636243 + -0.19 x = 0.549636243 + -0.19 Combine like terms: 0.549636243 + -0.19 = 0.359636243 x = 0.359636243 Simplifying x = 0.359636243Subproblem 2
x + 0.19 = -0.549636243 Simplifying x + 0.19 = -0.549636243 Reorder the terms: 0.19 + x = -0.549636243 Solving 0.19 + x = -0.549636243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.19' to each side of the equation. 0.19 + -0.19 + x = -0.549636243 + -0.19 Combine like terms: 0.19 + -0.19 = 0.00 0.00 + x = -0.549636243 + -0.19 x = -0.549636243 + -0.19 Combine like terms: -0.549636243 + -0.19 = -0.739636243 x = -0.739636243 Simplifying x = -0.739636243Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.359636243, -0.739636243}
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