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Simplifying 2x2 + -59x = 7x2 + -6x + -40 Reorder the terms: -59x + 2x2 = 7x2 + -6x + -40 Reorder the terms: -59x + 2x2 = -40 + -6x + 7x2 Solving -59x + 2x2 = -40 + -6x + 7x2 Solving for variable 'x'. Reorder the terms: 40 + -59x + 6x + 2x2 + -7x2 = -40 + -6x + 7x2 + 40 + 6x + -7x2 Combine like terms: -59x + 6x = -53x 40 + -53x + 2x2 + -7x2 = -40 + -6x + 7x2 + 40 + 6x + -7x2 Combine like terms: 2x2 + -7x2 = -5x2 40 + -53x + -5x2 = -40 + -6x + 7x2 + 40 + 6x + -7x2 Reorder the terms: 40 + -53x + -5x2 = -40 + 40 + -6x + 6x + 7x2 + -7x2 Combine like terms: -40 + 40 = 0 40 + -53x + -5x2 = 0 + -6x + 6x + 7x2 + -7x2 40 + -53x + -5x2 = -6x + 6x + 7x2 + -7x2 Combine like terms: -6x + 6x = 0 40 + -53x + -5x2 = 0 + 7x2 + -7x2 40 + -53x + -5x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 40 + -53x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -8 + 10.6x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 10.6x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 10.6x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 10.6x + x2 = 0 + 8 10.6x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 10.6x + x2 = 8 The x term is 10.6x. Take half its coefficient (5.3). Square it (28.09) and add it to both sides. Add '28.09' to each side of the equation. 10.6x + 28.09 + x2 = 8 + 28.09 Reorder the terms: 28.09 + 10.6x + x2 = 8 + 28.09 Combine like terms: 8 + 28.09 = 36.09 28.09 + 10.6x + x2 = 36.09 Factor a perfect square on the left side: (x + 5.3)(x + 5.3) = 36.09 Calculate the square root of the right side: 6.007495318 Break this problem into two subproblems by setting (x + 5.3) equal to 6.007495318 and -6.007495318.Subproblem 1
x + 5.3 = 6.007495318 Simplifying x + 5.3 = 6.007495318 Reorder the terms: 5.3 + x = 6.007495318 Solving 5.3 + x = 6.007495318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.3' to each side of the equation. 5.3 + -5.3 + x = 6.007495318 + -5.3 Combine like terms: 5.3 + -5.3 = 0.0 0.0 + x = 6.007495318 + -5.3 x = 6.007495318 + -5.3 Combine like terms: 6.007495318 + -5.3 = 0.707495318 x = 0.707495318 Simplifying x = 0.707495318Subproblem 2
x + 5.3 = -6.007495318 Simplifying x + 5.3 = -6.007495318 Reorder the terms: 5.3 + x = -6.007495318 Solving 5.3 + x = -6.007495318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.3' to each side of the equation. 5.3 + -5.3 + x = -6.007495318 + -5.3 Combine like terms: 5.3 + -5.3 = 0.0 0.0 + x = -6.007495318 + -5.3 x = -6.007495318 + -5.3 Combine like terms: -6.007495318 + -5.3 = -11.307495318 x = -11.307495318 Simplifying x = -11.307495318Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.707495318, -11.307495318}
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