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Simplifying 255x2 + -85.915x + 7.03545 = 0 Reorder the terms: 7.03545 + -85.915x + 255x2 = 0 Solving 7.03545 + -85.915x + 255x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 255 the coefficient of the squared term: Divide each side by '255'. 0.02759 + -0.3369215686x + x2 = 0 Move the constant term to the right: Add '-0.02759' to each side of the equation. 0.02759 + -0.3369215686x + -0.02759 + x2 = 0 + -0.02759 Reorder the terms: 0.02759 + -0.02759 + -0.3369215686x + x2 = 0 + -0.02759 Combine like terms: 0.02759 + -0.02759 = 0.00000 0.00000 + -0.3369215686x + x2 = 0 + -0.02759 -0.3369215686x + x2 = 0 + -0.02759 Combine like terms: 0 + -0.02759 = -0.02759 -0.3369215686x + x2 = -0.02759 The x term is -0.3369215686x. Take half its coefficient (-0.1684607843). Square it (0.02837903585) and add it to both sides. Add '0.02837903585' to each side of the equation. -0.3369215686x + 0.02837903585 + x2 = -0.02759 + 0.02837903585 Reorder the terms: 0.02837903585 + -0.3369215686x + x2 = -0.02759 + 0.02837903585 Combine like terms: -0.02759 + 0.02837903585 = 0.00078903585 0.02837903585 + -0.3369215686x + x2 = 0.00078903585 Factor a perfect square on the left side: (x + -0.1684607843)(x + -0.1684607843) = 0.00078903585 Calculate the square root of the right side: 0.028089782 Break this problem into two subproblems by setting (x + -0.1684607843) equal to 0.028089782 and -0.028089782.Subproblem 1
x + -0.1684607843 = 0.028089782 Simplifying x + -0.1684607843 = 0.028089782 Reorder the terms: -0.1684607843 + x = 0.028089782 Solving -0.1684607843 + x = 0.028089782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1684607843' to each side of the equation. -0.1684607843 + 0.1684607843 + x = 0.028089782 + 0.1684607843 Combine like terms: -0.1684607843 + 0.1684607843 = 0.0000000000 0.0000000000 + x = 0.028089782 + 0.1684607843 x = 0.028089782 + 0.1684607843 Combine like terms: 0.028089782 + 0.1684607843 = 0.1965505663 x = 0.1965505663 Simplifying x = 0.1965505663Subproblem 2
x + -0.1684607843 = -0.028089782 Simplifying x + -0.1684607843 = -0.028089782 Reorder the terms: -0.1684607843 + x = -0.028089782 Solving -0.1684607843 + x = -0.028089782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1684607843' to each side of the equation. -0.1684607843 + 0.1684607843 + x = -0.028089782 + 0.1684607843 Combine like terms: -0.1684607843 + 0.1684607843 = 0.0000000000 0.0000000000 + x = -0.028089782 + 0.1684607843 x = -0.028089782 + 0.1684607843 Combine like terms: -0.028089782 + 0.1684607843 = 0.1403710023 x = 0.1403710023 Simplifying x = 0.1403710023Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1965505663, 0.1403710023}
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