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Simplifying 1.3x + 0.06x2 = 150 Solving 1.3x + 0.06x2 = 150 Solving for variable 'x'. Reorder the terms: -150 + 1.3x + 0.06x2 = 150 + -150 Combine like terms: 150 + -150 = 0 -150 + 1.3x + 0.06x2 = 0 Begin completing the square. Divide all terms by 0.06 the coefficient of the squared term: Divide each side by '0.06'. -2500 + 21.66666667x + x2 = 0 Move the constant term to the right: Add '2500' to each side of the equation. -2500 + 21.66666667x + 2500 + x2 = 0 + 2500 Reorder the terms: -2500 + 2500 + 21.66666667x + x2 = 0 + 2500 Combine like terms: -2500 + 2500 = 0 0 + 21.66666667x + x2 = 0 + 2500 21.66666667x + x2 = 0 + 2500 Combine like terms: 0 + 2500 = 2500 21.66666667x + x2 = 2500 The x term is 21.66666667x. Take half its coefficient (10.83333334). Square it (117.3611113) and add it to both sides. Add '117.3611113' to each side of the equation. 21.66666667x + 117.3611113 + x2 = 2500 + 117.3611113 Reorder the terms: 117.3611113 + 21.66666667x + x2 = 2500 + 117.3611113 Combine like terms: 2500 + 117.3611113 = 2617.3611113 117.3611113 + 21.66666667x + x2 = 2617.3611113 Factor a perfect square on the left side: (x + 10.83333334)(x + 10.83333334) = 2617.3611113 Calculate the square root of the right side: 51.160151596 Break this problem into two subproblems by setting (x + 10.83333334) equal to 51.160151596 and -51.160151596.Subproblem 1
x + 10.83333334 = 51.160151596 Simplifying x + 10.83333334 = 51.160151596 Reorder the terms: 10.83333334 + x = 51.160151596 Solving 10.83333334 + x = 51.160151596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.83333334' to each side of the equation. 10.83333334 + -10.83333334 + x = 51.160151596 + -10.83333334 Combine like terms: 10.83333334 + -10.83333334 = 0.00000000 0.00000000 + x = 51.160151596 + -10.83333334 x = 51.160151596 + -10.83333334 Combine like terms: 51.160151596 + -10.83333334 = 40.326818256 x = 40.326818256 Simplifying x = 40.326818256Subproblem 2
x + 10.83333334 = -51.160151596 Simplifying x + 10.83333334 = -51.160151596 Reorder the terms: 10.83333334 + x = -51.160151596 Solving 10.83333334 + x = -51.160151596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.83333334' to each side of the equation. 10.83333334 + -10.83333334 + x = -51.160151596 + -10.83333334 Combine like terms: 10.83333334 + -10.83333334 = 0.00000000 0.00000000 + x = -51.160151596 + -10.83333334 x = -51.160151596 + -10.83333334 Combine like terms: -51.160151596 + -10.83333334 = -61.993484936 x = -61.993484936 Simplifying x = -61.993484936Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.326818256, -61.993484936}
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