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Simplifying 5x2 + -4x + 1 = 3x + 4 Reorder the terms: 1 + -4x + 5x2 = 3x + 4 Reorder the terms: 1 + -4x + 5x2 = 4 + 3x Solving 1 + -4x + 5x2 = 4 + 3x Solving for variable 'x'. Reorder the terms: 1 + -4 + -4x + -3x + 5x2 = 4 + 3x + -4 + -3x Combine like terms: 1 + -4 = -3 -3 + -4x + -3x + 5x2 = 4 + 3x + -4 + -3x Combine like terms: -4x + -3x = -7x -3 + -7x + 5x2 = 4 + 3x + -4 + -3x Reorder the terms: -3 + -7x + 5x2 = 4 + -4 + 3x + -3x Combine like terms: 4 + -4 = 0 -3 + -7x + 5x2 = 0 + 3x + -3x -3 + -7x + 5x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -3 + -7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + -1.4x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -1.4x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -1.4x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -1.4x + x2 = 0 + 0.6 -1.4x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -1.4x + x2 = 0.6 The x term is -1.4x. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4x + 0.49 + x2 = 0.6 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = 0.6 + 0.49 Combine like terms: 0.6 + 0.49 = 1.09 0.49 + -1.4x + x2 = 1.09 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 1.09 Calculate the square root of the right side: 1.044030651 Break this problem into two subproblems by setting (x + -0.7) equal to 1.044030651 and -1.044030651.Subproblem 1
x + -0.7 = 1.044030651 Simplifying x + -0.7 = 1.044030651 Reorder the terms: -0.7 + x = 1.044030651 Solving -0.7 + x = 1.044030651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = 1.044030651 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 1.044030651 + 0.7 x = 1.044030651 + 0.7 Combine like terms: 1.044030651 + 0.7 = 1.744030651 x = 1.744030651 Simplifying x = 1.744030651Subproblem 2
x + -0.7 = -1.044030651 Simplifying x + -0.7 = -1.044030651 Reorder the terms: -0.7 + x = -1.044030651 Solving -0.7 + x = -1.044030651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = -1.044030651 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -1.044030651 + 0.7 x = -1.044030651 + 0.7 Combine like terms: -1.044030651 + 0.7 = -0.344030651 x = -0.344030651 Simplifying x = -0.344030651Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.744030651, -0.344030651}
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