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Simplifying x2 + 0.304x + -0.231 = 0 Reorder the terms: -0.231 + 0.304x + x2 = 0 Solving -0.231 + 0.304x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.231' to each side of the equation. -0.231 + 0.304x + 0.231 + x2 = 0 + 0.231 Reorder the terms: -0.231 + 0.231 + 0.304x + x2 = 0 + 0.231 Combine like terms: -0.231 + 0.231 = 0.000 0.000 + 0.304x + x2 = 0 + 0.231 0.304x + x2 = 0 + 0.231 Combine like terms: 0 + 0.231 = 0.231 0.304x + x2 = 0.231 The x term is 0.304x. Take half its coefficient (0.152). Square it (0.023104) and add it to both sides. Add '0.023104' to each side of the equation. 0.304x + 0.023104 + x2 = 0.231 + 0.023104 Reorder the terms: 0.023104 + 0.304x + x2 = 0.231 + 0.023104 Combine like terms: 0.231 + 0.023104 = 0.254104 0.023104 + 0.304x + x2 = 0.254104 Factor a perfect square on the left side: (x + 0.152)(x + 0.152) = 0.254104 Calculate the square root of the right side: 0.504087294 Break this problem into two subproblems by setting (x + 0.152) equal to 0.504087294 and -0.504087294.Subproblem 1
x + 0.152 = 0.504087294 Simplifying x + 0.152 = 0.504087294 Reorder the terms: 0.152 + x = 0.504087294 Solving 0.152 + x = 0.504087294 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.152' to each side of the equation. 0.152 + -0.152 + x = 0.504087294 + -0.152 Combine like terms: 0.152 + -0.152 = 0.000 0.000 + x = 0.504087294 + -0.152 x = 0.504087294 + -0.152 Combine like terms: 0.504087294 + -0.152 = 0.352087294 x = 0.352087294 Simplifying x = 0.352087294Subproblem 2
x + 0.152 = -0.504087294 Simplifying x + 0.152 = -0.504087294 Reorder the terms: 0.152 + x = -0.504087294 Solving 0.152 + x = -0.504087294 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.152' to each side of the equation. 0.152 + -0.152 + x = -0.504087294 + -0.152 Combine like terms: 0.152 + -0.152 = 0.000 0.000 + x = -0.504087294 + -0.152 x = -0.504087294 + -0.152 Combine like terms: -0.504087294 + -0.152 = -0.656087294 x = -0.656087294 Simplifying x = -0.656087294Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.352087294, -0.656087294}
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