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Simplifying 21x2 + 28x + 2 = 0 Reorder the terms: 2 + 28x + 21x2 = 0 Solving 2 + 28x + 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'. 0.09523809524 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '-0.09523809524' to each side of the equation. 0.09523809524 + 1.333333333x + -0.09523809524 + x2 = 0 + -0.09523809524 Reorder the terms: 0.09523809524 + -0.09523809524 + 1.333333333x + x2 = 0 + -0.09523809524 Combine like terms: 0.09523809524 + -0.09523809524 = 0.00000000000 0.00000000000 + 1.333333333x + x2 = 0 + -0.09523809524 1.333333333x + x2 = 0 + -0.09523809524 Combine like terms: 0 + -0.09523809524 = -0.09523809524 1.333333333x + x2 = -0.09523809524 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = -0.09523809524 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = -0.09523809524 + 0.4444444442 Combine like terms: -0.09523809524 + 0.4444444442 = 0.34920634896 0.4444444442 + 1.333333333x + x2 = 0.34920634896 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 0.34920634896 Calculate the square root of the right side: 0.59093684 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 0.59093684 and -0.59093684.Subproblem 1
x + 0.6666666665 = 0.59093684 Simplifying x + 0.6666666665 = 0.59093684 Reorder the terms: 0.6666666665 + x = 0.59093684 Solving 0.6666666665 + x = 0.59093684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 0.59093684 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 0.59093684 + -0.6666666665 x = 0.59093684 + -0.6666666665 Combine like terms: 0.59093684 + -0.6666666665 = -0.0757298265 x = -0.0757298265 Simplifying x = -0.0757298265Subproblem 2
x + 0.6666666665 = -0.59093684 Simplifying x + 0.6666666665 = -0.59093684 Reorder the terms: 0.6666666665 + x = -0.59093684 Solving 0.6666666665 + x = -0.59093684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -0.59093684 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -0.59093684 + -0.6666666665 x = -0.59093684 + -0.6666666665 Combine like terms: -0.59093684 + -0.6666666665 = -1.2576035065 x = -1.2576035065 Simplifying x = -1.2576035065Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0757298265, -1.2576035065}
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