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Simplifying 0 = -3x2 + 5x + 7 Reorder the terms: 0 = 7 + 5x + -3x2 Solving 0 = 7 + 5x + -3x2 Solving for variable 'x'. Combine like terms: 0 + -7 = -7 -7 + -5x + 3x2 = 7 + 5x + -3x2 + -7 + -5x + 3x2 Reorder the terms: -7 + -5x + 3x2 = 7 + -7 + 5x + -5x + -3x2 + 3x2 Combine like terms: 7 + -7 = 0 -7 + -5x + 3x2 = 0 + 5x + -5x + -3x2 + 3x2 -7 + -5x + 3x2 = 5x + -5x + -3x2 + 3x2 Combine like terms: 5x + -5x = 0 -7 + -5x + 3x2 = 0 + -3x2 + 3x2 -7 + -5x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -7 + -5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.333333333 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + -1.666666667x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + -1.666666667x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + -1.666666667x + x2 = 0 + 2.333333333 -1.666666667x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 -1.666666667x + x2 = 2.333333333 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = 2.333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 2.333333333 + 0.6944444447 Combine like terms: 2.333333333 + 0.6944444447 = 3.0277777777 0.6944444447 + -1.666666667x + x2 = 3.0277777777 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 3.0277777777 Calculate the square root of the right side: 1.740051085 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 1.740051085 and -1.740051085.Subproblem 1
x + -0.8333333335 = 1.740051085 Simplifying x + -0.8333333335 = 1.740051085 Reorder the terms: -0.8333333335 + x = 1.740051085 Solving -0.8333333335 + x = 1.740051085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 1.740051085 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 1.740051085 + 0.8333333335 x = 1.740051085 + 0.8333333335 Combine like terms: 1.740051085 + 0.8333333335 = 2.5733844185 x = 2.5733844185 Simplifying x = 2.5733844185Subproblem 2
x + -0.8333333335 = -1.740051085 Simplifying x + -0.8333333335 = -1.740051085 Reorder the terms: -0.8333333335 + x = -1.740051085 Solving -0.8333333335 + x = -1.740051085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -1.740051085 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -1.740051085 + 0.8333333335 x = -1.740051085 + 0.8333333335 Combine like terms: -1.740051085 + 0.8333333335 = -0.9067177515 x = -0.9067177515 Simplifying x = -0.9067177515Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5733844185, -0.9067177515}
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