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Simplifying x2 + 0.43x + -4.0764 = 0 Reorder the terms: -4.0764 + 0.43x + x2 = 0 Solving -4.0764 + 0.43x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4.0764' to each side of the equation. -4.0764 + 0.43x + 4.0764 + x2 = 0 + 4.0764 Reorder the terms: -4.0764 + 4.0764 + 0.43x + x2 = 0 + 4.0764 Combine like terms: -4.0764 + 4.0764 = 0.0000 0.0000 + 0.43x + x2 = 0 + 4.0764 0.43x + x2 = 0 + 4.0764 Combine like terms: 0 + 4.0764 = 4.0764 0.43x + x2 = 4.0764 The x term is 0.43x. Take half its coefficient (0.215). Square it (0.046225) and add it to both sides. Add '0.046225' to each side of the equation. 0.43x + 0.046225 + x2 = 4.0764 + 0.046225 Reorder the terms: 0.046225 + 0.43x + x2 = 4.0764 + 0.046225 Combine like terms: 4.0764 + 0.046225 = 4.122625 0.046225 + 0.43x + x2 = 4.122625 Factor a perfect square on the left side: (x + 0.215)(x + 0.215) = 4.122625 Calculate the square root of the right side: 2.030424832 Break this problem into two subproblems by setting (x + 0.215) equal to 2.030424832 and -2.030424832.Subproblem 1
x + 0.215 = 2.030424832 Simplifying x + 0.215 = 2.030424832 Reorder the terms: 0.215 + x = 2.030424832 Solving 0.215 + x = 2.030424832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.215' to each side of the equation. 0.215 + -0.215 + x = 2.030424832 + -0.215 Combine like terms: 0.215 + -0.215 = 0.000 0.000 + x = 2.030424832 + -0.215 x = 2.030424832 + -0.215 Combine like terms: 2.030424832 + -0.215 = 1.815424832 x = 1.815424832 Simplifying x = 1.815424832Subproblem 2
x + 0.215 = -2.030424832 Simplifying x + 0.215 = -2.030424832 Reorder the terms: 0.215 + x = -2.030424832 Solving 0.215 + x = -2.030424832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.215' to each side of the equation. 0.215 + -0.215 + x = -2.030424832 + -0.215 Combine like terms: 0.215 + -0.215 = 0.000 0.000 + x = -2.030424832 + -0.215 x = -2.030424832 + -0.215 Combine like terms: -2.030424832 + -0.215 = -2.245424832 x = -2.245424832 Simplifying x = -2.245424832Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.815424832, -2.245424832}
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