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Simplifying 0 = -5x2 + 7x + 5 Reorder the terms: 0 = 5 + 7x + -5x2 Solving 0 = 5 + 7x + -5x2 Solving for variable 'x'. Combine like terms: 0 + -5 = -5 -5 + -7x + 5x2 = 5 + 7x + -5x2 + -5 + -7x + 5x2 Reorder the terms: -5 + -7x + 5x2 = 5 + -5 + 7x + -7x + -5x2 + 5x2 Combine like terms: 5 + -5 = 0 -5 + -7x + 5x2 = 0 + 7x + -7x + -5x2 + 5x2 -5 + -7x + 5x2 = 7x + -7x + -5x2 + 5x2 Combine like terms: 7x + -7x = 0 -5 + -7x + 5x2 = 0 + -5x2 + 5x2 -5 + -7x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -5 + -7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1 + -1.4x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.4x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -1.4x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.4x + x2 = 0 + 1 -1.4x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.4x + x2 = 1 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 = 1 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = 1 + 0.49 Combine like terms: 1 + 0.49 = 1.49 0.49 + -1.4x + x2 = 1.49 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 1.49 Calculate the square root of the right side: 1.220655562 Break this problem into two subproblems by setting (x + -0.7) equal to 1.220655562 and -1.220655562.Subproblem 1
x + -0.7 = 1.220655562 Simplifying x + -0.7 = 1.220655562 Reorder the terms: -0.7 + x = 1.220655562 Solving -0.7 + x = 1.220655562 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 = 1.220655562 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 1.220655562 + 0.7 x = 1.220655562 + 0.7 Combine like terms: 1.220655562 + 0.7 = 1.920655562 x = 1.920655562 Simplifying x = 1.920655562Subproblem 2
x + -0.7 = -1.220655562 Simplifying x + -0.7 = -1.220655562 Reorder the terms: -0.7 + x = -1.220655562 Solving -0.7 + x = -1.220655562 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 = -1.220655562 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -1.220655562 + 0.7 x = -1.220655562 + 0.7 Combine like terms: -1.220655562 + 0.7 = -0.520655562 x = -0.520655562 Simplifying x = -0.520655562Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.920655562, -0.520655562}
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