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Simplifying 0 = 3x2 + -40x + 75 Reorder the terms: 0 = 75 + -40x + 3x2 Solving 0 = 75 + -40x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -75 = -75 -75 + 40x + -3x2 = 75 + -40x + 3x2 + -75 + 40x + -3x2 Reorder the terms: -75 + 40x + -3x2 = 75 + -75 + -40x + 40x + 3x2 + -3x2 Combine like terms: 75 + -75 = 0 -75 + 40x + -3x2 = 0 + -40x + 40x + 3x2 + -3x2 -75 + 40x + -3x2 = -40x + 40x + 3x2 + -3x2 Combine like terms: -40x + 40x = 0 -75 + 40x + -3x2 = 0 + 3x2 + -3x2 -75 + 40x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -75 + 40x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 25 + -13.33333333x + x2 = 0 Move the constant term to the right: Add '-25' to each side of the equation. 25 + -13.33333333x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -13.33333333x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -13.33333333x + x2 = 0 + -25 -13.33333333x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -13.33333333x + x2 = -25 The x term is -13.33333333x. Take half its coefficient (-6.666666665). Square it (44.44444442) and add it to both sides. Add '44.44444442' to each side of the equation. -13.33333333x + 44.44444442 + x2 = -25 + 44.44444442 Reorder the terms: 44.44444442 + -13.33333333x + x2 = -25 + 44.44444442 Combine like terms: -25 + 44.44444442 = 19.44444442 44.44444442 + -13.33333333x + x2 = 19.44444442 Factor a perfect square on the left side: (x + -6.666666665)(x + -6.666666665) = 19.44444442 Calculate the square root of the right side: 4.409585516 Break this problem into two subproblems by setting (x + -6.666666665) equal to 4.409585516 and -4.409585516.Subproblem 1
x + -6.666666665 = 4.409585516 Simplifying x + -6.666666665 = 4.409585516 Reorder the terms: -6.666666665 + x = 4.409585516 Solving -6.666666665 + x = 4.409585516 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.666666665' to each side of the equation. -6.666666665 + 6.666666665 + x = 4.409585516 + 6.666666665 Combine like terms: -6.666666665 + 6.666666665 = 0.000000000 0.000000000 + x = 4.409585516 + 6.666666665 x = 4.409585516 + 6.666666665 Combine like terms: 4.409585516 + 6.666666665 = 11.076252181 x = 11.076252181 Simplifying x = 11.076252181Subproblem 2
x + -6.666666665 = -4.409585516 Simplifying x + -6.666666665 = -4.409585516 Reorder the terms: -6.666666665 + x = -4.409585516 Solving -6.666666665 + x = -4.409585516 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.666666665' to each side of the equation. -6.666666665 + 6.666666665 + x = -4.409585516 + 6.666666665 Combine like terms: -6.666666665 + 6.666666665 = 0.000000000 0.000000000 + x = -4.409585516 + 6.666666665 x = -4.409585516 + 6.666666665 Combine like terms: -4.409585516 + 6.666666665 = 2.257081149 x = 2.257081149 Simplifying x = 2.257081149Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.076252181, 2.257081149}
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