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Simplifying 3x2 + -5x = 15 Reorder the terms: -5x + 3x2 = 15 Solving -5x + 3x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + -5x + 3x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + -5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -1.666666667x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -1.666666667x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1.666666667x + x2 = 0 + 5 -1.666666667x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -1.666666667x + x2 = 5 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 = 5 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 5 + 0.6944444447 Combine like terms: 5 + 0.6944444447 = 5.6944444447 0.6944444447 + -1.666666667x + x2 = 5.6944444447 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 5.6944444447 Calculate the square root of the right side: 2.386303511 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 2.386303511 and -2.386303511.Subproblem 1
x + -0.8333333335 = 2.386303511 Simplifying x + -0.8333333335 = 2.386303511 Reorder the terms: -0.8333333335 + x = 2.386303511 Solving -0.8333333335 + x = 2.386303511 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 = 2.386303511 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 2.386303511 + 0.8333333335 x = 2.386303511 + 0.8333333335 Combine like terms: 2.386303511 + 0.8333333335 = 3.2196368445 x = 3.2196368445 Simplifying x = 3.2196368445Subproblem 2
x + -0.8333333335 = -2.386303511 Simplifying x + -0.8333333335 = -2.386303511 Reorder the terms: -0.8333333335 + x = -2.386303511 Solving -0.8333333335 + x = -2.386303511 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 = -2.386303511 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -2.386303511 + 0.8333333335 x = -2.386303511 + 0.8333333335 Combine like terms: -2.386303511 + 0.8333333335 = -1.5529701775 x = -1.5529701775 Simplifying x = -1.5529701775Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.2196368445, -1.5529701775}
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