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Simplifying 21x2 + 14x + -5 = 0 Reorder the terms: -5 + 14x + 21x2 = 0 Solving -5 + 14x + 21x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -0.2380952381 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '0.2380952381' to each side of the equation. -0.2380952381 + 0.6666666667x + 0.2380952381 + x2 = 0 + 0.2380952381 Reorder the terms: -0.2380952381 + 0.2380952381 + 0.6666666667x + x2 = 0 + 0.2380952381 Combine like terms: -0.2380952381 + 0.2380952381 = 0.0000000000 0.0000000000 + 0.6666666667x + x2 = 0 + 0.2380952381 0.6666666667x + x2 = 0 + 0.2380952381 Combine like terms: 0 + 0.2380952381 = 0.2380952381 0.6666666667x + x2 = 0.2380952381 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 0.2380952381 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 0.2380952381 + 0.1111111112 Combine like terms: 0.2380952381 + 0.1111111112 = 0.3492063493 0.1111111112 + 0.6666666667x + x2 = 0.3492063493 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 0.3492063493 Calculate the square root of the right side: 0.59093684 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 0.59093684 and -0.59093684.Subproblem 1
x + 0.3333333334 = 0.59093684 Simplifying x + 0.3333333334 = 0.59093684 Reorder the terms: 0.3333333334 + x = 0.59093684 Solving 0.3333333334 + x = 0.59093684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 0.59093684 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 0.59093684 + -0.3333333334 x = 0.59093684 + -0.3333333334 Combine like terms: 0.59093684 + -0.3333333334 = 0.2576035066 x = 0.2576035066 Simplifying x = 0.2576035066Subproblem 2
x + 0.3333333334 = -0.59093684 Simplifying x + 0.3333333334 = -0.59093684 Reorder the terms: 0.3333333334 + x = -0.59093684 Solving 0.3333333334 + x = -0.59093684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -0.59093684 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -0.59093684 + -0.3333333334 x = -0.59093684 + -0.3333333334 Combine like terms: -0.59093684 + -0.3333333334 = -0.9242701734 x = -0.9242701734 Simplifying x = -0.9242701734Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2576035066, -0.9242701734}
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