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Simplifying x2 + 0.45x + -0.45 = 0 Reorder the terms: -0.45 + 0.45x + x2 = 0 Solving -0.45 + 0.45x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.45' to each side of the equation. -0.45 + 0.45x + 0.45 + x2 = 0 + 0.45 Reorder the terms: -0.45 + 0.45 + 0.45x + x2 = 0 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + 0.45x + x2 = 0 + 0.45 0.45x + x2 = 0 + 0.45 Combine like terms: 0 + 0.45 = 0.45 0.45x + x2 = 0.45 The x term is 0.45x. Take half its coefficient (0.225). Square it (0.050625) and add it to both sides. Add '0.050625' to each side of the equation. 0.45x + 0.050625 + x2 = 0.45 + 0.050625 Reorder the terms: 0.050625 + 0.45x + x2 = 0.45 + 0.050625 Combine like terms: 0.45 + 0.050625 = 0.500625 0.050625 + 0.45x + x2 = 0.500625 Factor a perfect square on the left side: (x + 0.225)(x + 0.225) = 0.500625 Calculate the square root of the right side: 0.707548585 Break this problem into two subproblems by setting (x + 0.225) equal to 0.707548585 and -0.707548585.Subproblem 1
x + 0.225 = 0.707548585 Simplifying x + 0.225 = 0.707548585 Reorder the terms: 0.225 + x = 0.707548585 Solving 0.225 + x = 0.707548585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.225' to each side of the equation. 0.225 + -0.225 + x = 0.707548585 + -0.225 Combine like terms: 0.225 + -0.225 = 0.000 0.000 + x = 0.707548585 + -0.225 x = 0.707548585 + -0.225 Combine like terms: 0.707548585 + -0.225 = 0.482548585 x = 0.482548585 Simplifying x = 0.482548585Subproblem 2
x + 0.225 = -0.707548585 Simplifying x + 0.225 = -0.707548585 Reorder the terms: 0.225 + x = -0.707548585 Solving 0.225 + x = -0.707548585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.225' to each side of the equation. 0.225 + -0.225 + x = -0.707548585 + -0.225 Combine like terms: 0.225 + -0.225 = 0.000 0.000 + x = -0.707548585 + -0.225 x = -0.707548585 + -0.225 Combine like terms: -0.707548585 + -0.225 = -0.932548585 x = -0.932548585 Simplifying x = -0.932548585Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.482548585, -0.932548585}
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