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Simplifying (3x2) + 14x = 21 Reorder the terms: 14x + (3x2) = 21 Solving 14x + (3x2) = 21 Solving for variable 'x'. Reorder the terms: -21 + 14x + (3x2) = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + 14x + (3x2) = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -7 + 4.666666667x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 4.666666667x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 4.666666667x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 4.666666667x + x2 = 0 + 7 4.666666667x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 4.666666667x + x2 = 7 The x term is 4.666666667x. Take half its coefficient (2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. 4.666666667x + 5.444444448 + x2 = 7 + 5.444444448 Reorder the terms: 5.444444448 + 4.666666667x + x2 = 7 + 5.444444448 Combine like terms: 7 + 5.444444448 = 12.444444448 5.444444448 + 4.666666667x + x2 = 12.444444448 Factor a perfect square on the left side: ((x) + 2.333333334)((x) + 2.333333334) = 12.444444448 Calculate the square root of the right side: 3.527668415 Break this problem into two subproblems by setting ((x) + 2.333333334) equal to 3.527668415 and -3.527668415.Subproblem 1
(x) + 2.333333334 = 3.527668415 Simplifying (x) + 2.333333334 = 3.527668415 x + 2.333333334 = 3.527668415 Reorder the terms: 2.333333334 + x = 3.527668415 Solving 2.333333334 + x = 3.527668415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = 3.527668415 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = 3.527668415 + -2.333333334 x = 3.527668415 + -2.333333334 Combine like terms: 3.527668415 + -2.333333334 = 1.194335081 x = 1.194335081 Simplifying x = 1.194335081Subproblem 2
(x) + 2.333333334 = -3.527668415 Simplifying (x) + 2.333333334 = -3.527668415 x + 2.333333334 = -3.527668415 Reorder the terms: 2.333333334 + x = -3.527668415 Solving 2.333333334 + x = -3.527668415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = -3.527668415 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = -3.527668415 + -2.333333334 x = -3.527668415 + -2.333333334 Combine like terms: -3.527668415 + -2.333333334 = -5.861001749 x = -5.861001749 Simplifying x = -5.861001749Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.194335081, -5.861001749}
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