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Simplifying 21x2 + 144x + 215 = 0 Reorder the terms: 215 + 144x + 21x2 = 0 Solving 215 + 144x + 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'. 10.23809524 + 6.857142857x + x2 = 0 Move the constant term to the right: Add '-10.23809524' to each side of the equation. 10.23809524 + 6.857142857x + -10.23809524 + x2 = 0 + -10.23809524 Reorder the terms: 10.23809524 + -10.23809524 + 6.857142857x + x2 = 0 + -10.23809524 Combine like terms: 10.23809524 + -10.23809524 = 0.00000000 0.00000000 + 6.857142857x + x2 = 0 + -10.23809524 6.857142857x + x2 = 0 + -10.23809524 Combine like terms: 0 + -10.23809524 = -10.23809524 6.857142857x + x2 = -10.23809524 The x term is 6.857142857x. Take half its coefficient (3.428571429). Square it (11.75510204) and add it to both sides. Add '11.75510204' to each side of the equation. 6.857142857x + 11.75510204 + x2 = -10.23809524 + 11.75510204 Reorder the terms: 11.75510204 + 6.857142857x + x2 = -10.23809524 + 11.75510204 Combine like terms: -10.23809524 + 11.75510204 = 1.5170068 11.75510204 + 6.857142857x + x2 = 1.5170068 Factor a perfect square on the left side: (x + 3.428571429)(x + 3.428571429) = 1.5170068 Calculate the square root of the right side: 1.2316683 Break this problem into two subproblems by setting (x + 3.428571429) equal to 1.2316683 and -1.2316683.Subproblem 1
x + 3.428571429 = 1.2316683 Simplifying x + 3.428571429 = 1.2316683 Reorder the terms: 3.428571429 + x = 1.2316683 Solving 3.428571429 + x = 1.2316683 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.428571429' to each side of the equation. 3.428571429 + -3.428571429 + x = 1.2316683 + -3.428571429 Combine like terms: 3.428571429 + -3.428571429 = 0.000000000 0.000000000 + x = 1.2316683 + -3.428571429 x = 1.2316683 + -3.428571429 Combine like terms: 1.2316683 + -3.428571429 = -2.196903129 x = -2.196903129 Simplifying x = -2.196903129Subproblem 2
x + 3.428571429 = -1.2316683 Simplifying x + 3.428571429 = -1.2316683 Reorder the terms: 3.428571429 + x = -1.2316683 Solving 3.428571429 + x = -1.2316683 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.428571429' to each side of the equation. 3.428571429 + -3.428571429 + x = -1.2316683 + -3.428571429 Combine like terms: 3.428571429 + -3.428571429 = 0.000000000 0.000000000 + x = -1.2316683 + -3.428571429 x = -1.2316683 + -3.428571429 Combine like terms: -1.2316683 + -3.428571429 = -4.660239729 x = -4.660239729 Simplifying x = -4.660239729Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.196903129, -4.660239729}
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