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Simplifying 5x * 5x + 14x + -3 = 0 Reorder the terms for easier multiplication: 5 * 5x * x + 14x + -3 = 0 Multiply 5 * 5 25x * x + 14x + -3 = 0 Multiply x * x 25x2 + 14x + -3 = 0 Reorder the terms: -3 + 14x + 25x2 = 0 Solving -3 + 14x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.12 + 0.56x + x2 = 0 Move the constant term to the right: Add '0.12' to each side of the equation. -0.12 + 0.56x + 0.12 + x2 = 0 + 0.12 Reorder the terms: -0.12 + 0.12 + 0.56x + x2 = 0 + 0.12 Combine like terms: -0.12 + 0.12 = 0.00 0.00 + 0.56x + x2 = 0 + 0.12 0.56x + x2 = 0 + 0.12 Combine like terms: 0 + 0.12 = 0.12 0.56x + x2 = 0.12 The x term is 0.56x. Take half its coefficient (0.28). Square it (0.0784) and add it to both sides. Add '0.0784' to each side of the equation. 0.56x + 0.0784 + x2 = 0.12 + 0.0784 Reorder the terms: 0.0784 + 0.56x + x2 = 0.12 + 0.0784 Combine like terms: 0.12 + 0.0784 = 0.1984 0.0784 + 0.56x + x2 = 0.1984 Factor a perfect square on the left side: (x + 0.28)(x + 0.28) = 0.1984 Calculate the square root of the right side: 0.445421149 Break this problem into two subproblems by setting (x + 0.28) equal to 0.445421149 and -0.445421149.Subproblem 1
x + 0.28 = 0.445421149 Simplifying x + 0.28 = 0.445421149 Reorder the terms: 0.28 + x = 0.445421149 Solving 0.28 + x = 0.445421149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.28' to each side of the equation. 0.28 + -0.28 + x = 0.445421149 + -0.28 Combine like terms: 0.28 + -0.28 = 0.00 0.00 + x = 0.445421149 + -0.28 x = 0.445421149 + -0.28 Combine like terms: 0.445421149 + -0.28 = 0.165421149 x = 0.165421149 Simplifying x = 0.165421149Subproblem 2
x + 0.28 = -0.445421149 Simplifying x + 0.28 = -0.445421149 Reorder the terms: 0.28 + x = -0.445421149 Solving 0.28 + x = -0.445421149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.28' to each side of the equation. 0.28 + -0.28 + x = -0.445421149 + -0.28 Combine like terms: 0.28 + -0.28 = 0.00 0.00 + x = -0.445421149 + -0.28 x = -0.445421149 + -0.28 Combine like terms: -0.445421149 + -0.28 = -0.725421149 x = -0.725421149 Simplifying x = -0.725421149Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.165421149, -0.725421149}
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