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Simplifying 3x2 + -23x = 28 Reorder the terms: -23x + 3x2 = 28 Solving -23x + 3x2 = 28 Solving for variable 'x'. Reorder the terms: -28 + -23x + 3x2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + -23x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -9.333333333 + -7.666666667x + x2 = 0 Move the constant term to the right: Add '9.333333333' to each side of the equation. -9.333333333 + -7.666666667x + 9.333333333 + x2 = 0 + 9.333333333 Reorder the terms: -9.333333333 + 9.333333333 + -7.666666667x + x2 = 0 + 9.333333333 Combine like terms: -9.333333333 + 9.333333333 = 0.000000000 0.000000000 + -7.666666667x + x2 = 0 + 9.333333333 -7.666666667x + x2 = 0 + 9.333333333 Combine like terms: 0 + 9.333333333 = 9.333333333 -7.666666667x + x2 = 9.333333333 The x term is -7.666666667x. Take half its coefficient (-3.833333334). Square it (14.69444445) and add it to both sides. Add '14.69444445' to each side of the equation. -7.666666667x + 14.69444445 + x2 = 9.333333333 + 14.69444445 Reorder the terms: 14.69444445 + -7.666666667x + x2 = 9.333333333 + 14.69444445 Combine like terms: 9.333333333 + 14.69444445 = 24.027777783 14.69444445 + -7.666666667x + x2 = 24.027777783 Factor a perfect square on the left side: (x + -3.833333334)(x + -3.833333334) = 24.027777783 Calculate the square root of the right side: 4.901813724 Break this problem into two subproblems by setting (x + -3.833333334) equal to 4.901813724 and -4.901813724.Subproblem 1
x + -3.833333334 = 4.901813724 Simplifying x + -3.833333334 = 4.901813724 Reorder the terms: -3.833333334 + x = 4.901813724 Solving -3.833333334 + x = 4.901813724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = 4.901813724 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = 4.901813724 + 3.833333334 x = 4.901813724 + 3.833333334 Combine like terms: 4.901813724 + 3.833333334 = 8.735147058 x = 8.735147058 Simplifying x = 8.735147058Subproblem 2
x + -3.833333334 = -4.901813724 Simplifying x + -3.833333334 = -4.901813724 Reorder the terms: -3.833333334 + x = -4.901813724 Solving -3.833333334 + x = -4.901813724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = -4.901813724 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = -4.901813724 + 3.833333334 x = -4.901813724 + 3.833333334 Combine like terms: -4.901813724 + 3.833333334 = -1.06848039 x = -1.06848039 Simplifying x = -1.06848039Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.735147058, -1.06848039}
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