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Simplifying -6x2 + 15x = -7x + -21 Reorder the terms: 15x + -6x2 = -7x + -21 Reorder the terms: 15x + -6x2 = -21 + -7x Solving 15x + -6x2 = -21 + -7x Solving for variable 'x'. Reorder the terms: 21 + 15x + 7x + -6x2 = -21 + -7x + 21 + 7x Combine like terms: 15x + 7x = 22x 21 + 22x + -6x2 = -21 + -7x + 21 + 7x Reorder the terms: 21 + 22x + -6x2 = -21 + 21 + -7x + 7x Combine like terms: -21 + 21 = 0 21 + 22x + -6x2 = 0 + -7x + 7x 21 + 22x + -6x2 = -7x + 7x Combine like terms: -7x + 7x = 0 21 + 22x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -3.5 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -3.666666667x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -3.666666667x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -3.666666667x + x2 = 0 + 3.5 -3.666666667x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -3.666666667x + x2 = 3.5 The x term is -3.666666667x. Take half its coefficient (-1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. -3.666666667x + 3.361111114 + x2 = 3.5 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = 3.5 + 3.361111114 Combine like terms: 3.5 + 3.361111114 = 6.861111114 3.361111114 + -3.666666667x + x2 = 6.861111114 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 6.861111114 Calculate the square root of the right side: 2.619372275 Break this problem into two subproblems by setting (x + -1.833333334) equal to 2.619372275 and -2.619372275.Subproblem 1
x + -1.833333334 = 2.619372275 Simplifying x + -1.833333334 = 2.619372275 Reorder the terms: -1.833333334 + x = 2.619372275 Solving -1.833333334 + x = 2.619372275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = 2.619372275 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 2.619372275 + 1.833333334 x = 2.619372275 + 1.833333334 Combine like terms: 2.619372275 + 1.833333334 = 4.452705609 x = 4.452705609 Simplifying x = 4.452705609Subproblem 2
x + -1.833333334 = -2.619372275 Simplifying x + -1.833333334 = -2.619372275 Reorder the terms: -1.833333334 + x = -2.619372275 Solving -1.833333334 + x = -2.619372275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = -2.619372275 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -2.619372275 + 1.833333334 x = -2.619372275 + 1.833333334 Combine like terms: -2.619372275 + 1.833333334 = -0.786038941 x = -0.786038941 Simplifying x = -0.786038941Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.452705609, -0.786038941}
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