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Simplifying 3x2 + -40x + 100 = 625 Reorder the terms: 100 + -40x + 3x2 = 625 Solving 100 + -40x + 3x2 = 625 Solving for variable 'x'. Reorder the terms: 100 + -625 + -40x + 3x2 = 625 + -625 Combine like terms: 100 + -625 = -525 -525 + -40x + 3x2 = 625 + -625 Combine like terms: 625 + -625 = 0 -525 + -40x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -175 + -13.33333333x + x2 = 0 Move the constant term to the right: Add '175' to each side of the equation. -175 + -13.33333333x + 175 + x2 = 0 + 175 Reorder the terms: -175 + 175 + -13.33333333x + x2 = 0 + 175 Combine like terms: -175 + 175 = 0 0 + -13.33333333x + x2 = 0 + 175 -13.33333333x + x2 = 0 + 175 Combine like terms: 0 + 175 = 175 -13.33333333x + x2 = 175 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 = 175 + 44.44444442 Reorder the terms: 44.44444442 + -13.33333333x + x2 = 175 + 44.44444442 Combine like terms: 175 + 44.44444442 = 219.44444442 44.44444442 + -13.33333333x + x2 = 219.44444442 Factor a perfect square on the left side: (x + -6.666666665)(x + -6.666666665) = 219.44444442 Calculate the square root of the right side: 14.813657361 Break this problem into two subproblems by setting (x + -6.666666665) equal to 14.813657361 and -14.813657361.Subproblem 1
x + -6.666666665 = 14.813657361 Simplifying x + -6.666666665 = 14.813657361 Reorder the terms: -6.666666665 + x = 14.813657361 Solving -6.666666665 + x = 14.813657361 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 = 14.813657361 + 6.666666665 Combine like terms: -6.666666665 + 6.666666665 = 0.000000000 0.000000000 + x = 14.813657361 + 6.666666665 x = 14.813657361 + 6.666666665 Combine like terms: 14.813657361 + 6.666666665 = 21.480324026 x = 21.480324026 Simplifying x = 21.480324026Subproblem 2
x + -6.666666665 = -14.813657361 Simplifying x + -6.666666665 = -14.813657361 Reorder the terms: -6.666666665 + x = -14.813657361 Solving -6.666666665 + x = -14.813657361 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 = -14.813657361 + 6.666666665 Combine like terms: -6.666666665 + 6.666666665 = 0.000000000 0.000000000 + x = -14.813657361 + 6.666666665 x = -14.813657361 + 6.666666665 Combine like terms: -14.813657361 + 6.666666665 = -8.146990696 x = -8.146990696 Simplifying x = -8.146990696Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.480324026, -8.146990696}
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