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Simplifying 0.644 + -28.98x + 318x2 = 0 Solving 0.644 + -28.98x + 318x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 318 the coefficient of the squared term: Divide each side by '318'. 0.002025157233 + -0.09113207547x + x2 = 0 Move the constant term to the right: Add '-0.002025157233' to each side of the equation. 0.002025157233 + -0.09113207547x + -0.002025157233 + x2 = 0 + -0.002025157233 Reorder the terms: 0.002025157233 + -0.002025157233 + -0.09113207547x + x2 = 0 + -0.002025157233 Combine like terms: 0.002025157233 + -0.002025157233 = 0.000000000000 0.000000000000 + -0.09113207547x + x2 = 0 + -0.002025157233 -0.09113207547x + x2 = 0 + -0.002025157233 Combine like terms: 0 + -0.002025157233 = -0.002025157233 -0.09113207547x + x2 = -0.002025157233 The x term is -0.09113207547x. Take half its coefficient (-0.04556603774). Square it (0.002076263795) and add it to both sides. Add '0.002076263795' to each side of the equation. -0.09113207547x + 0.002076263795 + x2 = -0.002025157233 + 0.002076263795 Reorder the terms: 0.002076263795 + -0.09113207547x + x2 = -0.002025157233 + 0.002076263795 Combine like terms: -0.002025157233 + 0.002076263795 = 0.000051106562 0.002076263795 + -0.09113207547x + x2 = 0.000051106562 Factor a perfect square on the left side: (x + -0.04556603774)(x + -0.04556603774) = 0.000051106562 Calculate the square root of the right side: 0.007148885 Break this problem into two subproblems by setting (x + -0.04556603774) equal to 0.007148885 and -0.007148885.Subproblem 1
x + -0.04556603774 = 0.007148885 Simplifying x + -0.04556603774 = 0.007148885 Reorder the terms: -0.04556603774 + x = 0.007148885 Solving -0.04556603774 + x = 0.007148885 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04556603774' to each side of the equation. -0.04556603774 + 0.04556603774 + x = 0.007148885 + 0.04556603774 Combine like terms: -0.04556603774 + 0.04556603774 = 0.00000000000 0.00000000000 + x = 0.007148885 + 0.04556603774 x = 0.007148885 + 0.04556603774 Combine like terms: 0.007148885 + 0.04556603774 = 0.05271492274 x = 0.05271492274 Simplifying x = 0.05271492274Subproblem 2
x + -0.04556603774 = -0.007148885 Simplifying x + -0.04556603774 = -0.007148885 Reorder the terms: -0.04556603774 + x = -0.007148885 Solving -0.04556603774 + x = -0.007148885 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04556603774' to each side of the equation. -0.04556603774 + 0.04556603774 + x = -0.007148885 + 0.04556603774 Combine like terms: -0.04556603774 + 0.04556603774 = 0.00000000000 0.00000000000 + x = -0.007148885 + 0.04556603774 x = -0.007148885 + 0.04556603774 Combine like terms: -0.007148885 + 0.04556603774 = 0.03841715274 x = 0.03841715274 Simplifying x = 0.03841715274Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.05271492274, 0.03841715274}
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