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Simplifying 0 = 3x2 + 29x + -21 Reorder the terms: 0 = -21 + 29x + 3x2 Solving 0 = -21 + 29x + 3x2 Solving for variable 'x'. Combine like terms: 0 + 21 = 21 21 + -29x + -3x2 = -21 + 29x + 3x2 + 21 + -29x + -3x2 Reorder the terms: 21 + -29x + -3x2 = -21 + 21 + 29x + -29x + 3x2 + -3x2 Combine like terms: -21 + 21 = 0 21 + -29x + -3x2 = 0 + 29x + -29x + 3x2 + -3x2 21 + -29x + -3x2 = 29x + -29x + 3x2 + -3x2 Combine like terms: 29x + -29x = 0 21 + -29x + -3x2 = 0 + 3x2 + -3x2 21 + -29x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 21 + -29x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -7 + 9.666666667x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 9.666666667x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 9.666666667x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 9.666666667x + x2 = 0 + 7 9.666666667x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 9.666666667x + x2 = 7 The x term is 9.666666667x. Take half its coefficient (4.833333334). Square it (23.36111112) and add it to both sides. Add '23.36111112' to each side of the equation. 9.666666667x + 23.36111112 + x2 = 7 + 23.36111112 Reorder the terms: 23.36111112 + 9.666666667x + x2 = 7 + 23.36111112 Combine like terms: 7 + 23.36111112 = 30.36111112 23.36111112 + 9.666666667x + x2 = 30.36111112 Factor a perfect square on the left side: (x + 4.833333334)(x + 4.833333334) = 30.36111112 Calculate the square root of the right side: 5.510091752 Break this problem into two subproblems by setting (x + 4.833333334) equal to 5.510091752 and -5.510091752.Subproblem 1
x + 4.833333334 = 5.510091752 Simplifying x + 4.833333334 = 5.510091752 Reorder the terms: 4.833333334 + x = 5.510091752 Solving 4.833333334 + x = 5.510091752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.833333334' to each side of the equation. 4.833333334 + -4.833333334 + x = 5.510091752 + -4.833333334 Combine like terms: 4.833333334 + -4.833333334 = 0.000000000 0.000000000 + x = 5.510091752 + -4.833333334 x = 5.510091752 + -4.833333334 Combine like terms: 5.510091752 + -4.833333334 = 0.676758418 x = 0.676758418 Simplifying x = 0.676758418Subproblem 2
x + 4.833333334 = -5.510091752 Simplifying x + 4.833333334 = -5.510091752 Reorder the terms: 4.833333334 + x = -5.510091752 Solving 4.833333334 + x = -5.510091752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.833333334' to each side of the equation. 4.833333334 + -4.833333334 + x = -5.510091752 + -4.833333334 Combine like terms: 4.833333334 + -4.833333334 = 0.000000000 0.000000000 + x = -5.510091752 + -4.833333334 x = -5.510091752 + -4.833333334 Combine like terms: -5.510091752 + -4.833333334 = -10.343425086 x = -10.343425086 Simplifying x = -10.343425086Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.676758418, -10.343425086}
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