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Simplifying 45 = 5x2 + 23x Reorder the terms: 45 = 23x + 5x2 Solving 45 = 23x + 5x2 Solving for variable 'x'. Reorder the terms: 45 + -23x + -5x2 = 23x + -23x + 5x2 + -5x2 Combine like terms: 23x + -23x = 0 45 + -23x + -5x2 = 0 + 5x2 + -5x2 45 + -23x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 45 + -23x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -9 + 4.6x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 4.6x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 4.6x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 4.6x + x2 = 0 + 9 4.6x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 4.6x + x2 = 9 The x term is 4.6x. Take half its coefficient (2.3). Square it (5.29) and add it to both sides. Add '5.29' to each side of the equation. 4.6x + 5.29 + x2 = 9 + 5.29 Reorder the terms: 5.29 + 4.6x + x2 = 9 + 5.29 Combine like terms: 9 + 5.29 = 14.29 5.29 + 4.6x + x2 = 14.29 Factor a perfect square on the left side: (x + 2.3)(x + 2.3) = 14.29 Calculate the square root of the right side: 3.780211634 Break this problem into two subproblems by setting (x + 2.3) equal to 3.780211634 and -3.780211634.Subproblem 1
x + 2.3 = 3.780211634 Simplifying x + 2.3 = 3.780211634 Reorder the terms: 2.3 + x = 3.780211634 Solving 2.3 + x = 3.780211634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.3' to each side of the equation. 2.3 + -2.3 + x = 3.780211634 + -2.3 Combine like terms: 2.3 + -2.3 = 0.0 0.0 + x = 3.780211634 + -2.3 x = 3.780211634 + -2.3 Combine like terms: 3.780211634 + -2.3 = 1.480211634 x = 1.480211634 Simplifying x = 1.480211634Subproblem 2
x + 2.3 = -3.780211634 Simplifying x + 2.3 = -3.780211634 Reorder the terms: 2.3 + x = -3.780211634 Solving 2.3 + x = -3.780211634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.3' to each side of the equation. 2.3 + -2.3 + x = -3.780211634 + -2.3 Combine like terms: 2.3 + -2.3 = 0.0 0.0 + x = -3.780211634 + -2.3 x = -3.780211634 + -2.3 Combine like terms: -3.780211634 + -2.3 = -6.080211634 x = -6.080211634 Simplifying x = -6.080211634Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.480211634, -6.080211634}
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