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Simplifying 260 = 0.03x2 + 0.2x Reorder the terms: 260 = 0.2x + 0.03x2 Solving 260 = 0.2x + 0.03x2 Solving for variable 'x'. Reorder the terms: 260 + -0.2x + -0.03x2 = 0.2x + -0.2x + 0.03x2 + -0.03x2 Combine like terms: 0.2x + -0.2x = 0.0 260 + -0.2x + -0.03x2 = 0.0 + 0.03x2 + -0.03x2 260 + -0.2x + -0.03x2 = 0.03x2 + -0.03x2 Combine like terms: 0.03x2 + -0.03x2 = 0.00 260 + -0.2x + -0.03x2 = 0.00 Begin completing the square. Divide all terms by -0.03 the coefficient of the squared term: Divide each side by '-0.03'. -8666.666667 + 6.666666667x + x2 = 0 Move the constant term to the right: Add '8666.666667' to each side of the equation. -8666.666667 + 6.666666667x + 8666.666667 + x2 = 0 + 8666.666667 Reorder the terms: -8666.666667 + 8666.666667 + 6.666666667x + x2 = 0 + 8666.666667 Combine like terms: -8666.666667 + 8666.666667 = 0.000000 0.000000 + 6.666666667x + x2 = 0 + 8666.666667 6.666666667x + x2 = 0 + 8666.666667 Combine like terms: 0 + 8666.666667 = 8666.666667 6.666666667x + x2 = 8666.666667 The x term is 6.666666667x. Take half its coefficient (3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. 6.666666667x + 11.11111112 + x2 = 8666.666667 + 11.11111112 Reorder the terms: 11.11111112 + 6.666666667x + x2 = 8666.666667 + 11.11111112 Combine like terms: 8666.666667 + 11.11111112 = 8677.77777812 11.11111112 + 6.666666667x + x2 = 8677.77777812 Factor a perfect square on the left side: (x + 3.333333334)(x + 3.333333334) = 8677.77777812 Calculate the square root of the right side: 93.154590752 Break this problem into two subproblems by setting (x + 3.333333334) equal to 93.154590752 and -93.154590752.Subproblem 1
x + 3.333333334 = 93.154590752 Simplifying x + 3.333333334 = 93.154590752 Reorder the terms: 3.333333334 + x = 93.154590752 Solving 3.333333334 + x = 93.154590752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + x = 93.154590752 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = 93.154590752 + -3.333333334 x = 93.154590752 + -3.333333334 Combine like terms: 93.154590752 + -3.333333334 = 89.821257418 x = 89.821257418 Simplifying x = 89.821257418Subproblem 2
x + 3.333333334 = -93.154590752 Simplifying x + 3.333333334 = -93.154590752 Reorder the terms: 3.333333334 + x = -93.154590752 Solving 3.333333334 + x = -93.154590752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + x = -93.154590752 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = -93.154590752 + -3.333333334 x = -93.154590752 + -3.333333334 Combine like terms: -93.154590752 + -3.333333334 = -96.487924086 x = -96.487924086 Simplifying x = -96.487924086Solution
The solution to the problem is based on the solutions from the subproblems. x = {89.821257418, -96.487924086}
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