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Simplifying 5x2 + 3x + -2 = 5 Reorder the terms: -2 + 3x + 5x2 = 5 Solving -2 + 3x + 5x2 = 5 Solving for variable 'x'. Reorder the terms: -2 + -5 + 3x + 5x2 = 5 + -5 Combine like terms: -2 + -5 = -7 -7 + 3x + 5x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -7 + 3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + 0.6x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + 0.6x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + 0.6x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + 0.6x + x2 = 0 + 1.4 0.6x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 0.6x + x2 = 1.4 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 1.4 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 1.4 + 0.09 Combine like terms: 1.4 + 0.09 = 1.49 0.09 + 0.6x + x2 = 1.49 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 1.49 Calculate the square root of the right side: 1.220655562 Break this problem into two subproblems by setting (x + 0.3) equal to 1.220655562 and -1.220655562.Subproblem 1
x + 0.3 = 1.220655562 Simplifying x + 0.3 = 1.220655562 Reorder the terms: 0.3 + x = 1.220655562 Solving 0.3 + x = 1.220655562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 1.220655562 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 1.220655562 + -0.3 x = 1.220655562 + -0.3 Combine like terms: 1.220655562 + -0.3 = 0.920655562 x = 0.920655562 Simplifying x = 0.920655562Subproblem 2
x + 0.3 = -1.220655562 Simplifying x + 0.3 = -1.220655562 Reorder the terms: 0.3 + x = -1.220655562 Solving 0.3 + x = -1.220655562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -1.220655562 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -1.220655562 + -0.3 x = -1.220655562 + -0.3 Combine like terms: -1.220655562 + -0.3 = -1.520655562 x = -1.520655562 Simplifying x = -1.520655562Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.920655562, -1.520655562}
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