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Simplifying 81x2 + 8x + -24 = 9x Reorder the terms: -24 + 8x + 81x2 = 9x Solving -24 + 8x + 81x2 = 9x Solving for variable 'x'. Reorder the terms: -24 + 8x + -9x + 81x2 = 9x + -9x Combine like terms: 8x + -9x = -1x -24 + -1x + 81x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -24 + -1x + 81x2 = 0 Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. -0.2962962963 + -0.01234567901x + x2 = 0 Move the constant term to the right: Add '0.2962962963' to each side of the equation. -0.2962962963 + -0.01234567901x + 0.2962962963 + x2 = 0 + 0.2962962963 Reorder the terms: -0.2962962963 + 0.2962962963 + -0.01234567901x + x2 = 0 + 0.2962962963 Combine like terms: -0.2962962963 + 0.2962962963 = 0.0000000000 0.0000000000 + -0.01234567901x + x2 = 0 + 0.2962962963 -0.01234567901x + x2 = 0 + 0.2962962963 Combine like terms: 0 + 0.2962962963 = 0.2962962963 -0.01234567901x + x2 = 0.2962962963 The x term is -0.01234567901x. Take half its coefficient (-0.006172839505). Square it (0.00003810394755) and add it to both sides. Add '0.00003810394755' to each side of the equation. -0.01234567901x + 0.00003810394755 + x2 = 0.2962962963 + 0.00003810394755 Reorder the terms: 0.00003810394755 + -0.01234567901x + x2 = 0.2962962963 + 0.00003810394755 Combine like terms: 0.2962962963 + 0.00003810394755 = 0.29633440024755 0.00003810394755 + -0.01234567901x + x2 = 0.29633440024755 Factor a perfect square on the left side: (x + -0.006172839505)(x + -0.006172839505) = 0.29633440024755 Calculate the square root of the right side: 0.544366054 Break this problem into two subproblems by setting (x + -0.006172839505) equal to 0.544366054 and -0.544366054.Subproblem 1
x + -0.006172839505 = 0.544366054 Simplifying x + -0.006172839505 = 0.544366054 Reorder the terms: -0.006172839505 + x = 0.544366054 Solving -0.006172839505 + x = 0.544366054 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.006172839505' to each side of the equation. -0.006172839505 + 0.006172839505 + x = 0.544366054 + 0.006172839505 Combine like terms: -0.006172839505 + 0.006172839505 = 0.000000000000 0.000000000000 + x = 0.544366054 + 0.006172839505 x = 0.544366054 + 0.006172839505 Combine like terms: 0.544366054 + 0.006172839505 = 0.550538893505 x = 0.550538893505 Simplifying x = 0.550538893505Subproblem 2
x + -0.006172839505 = -0.544366054 Simplifying x + -0.006172839505 = -0.544366054 Reorder the terms: -0.006172839505 + x = -0.544366054 Solving -0.006172839505 + x = -0.544366054 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.006172839505' to each side of the equation. -0.006172839505 + 0.006172839505 + x = -0.544366054 + 0.006172839505 Combine like terms: -0.006172839505 + 0.006172839505 = 0.000000000000 0.000000000000 + x = -0.544366054 + 0.006172839505 x = -0.544366054 + 0.006172839505 Combine like terms: -0.544366054 + 0.006172839505 = -0.538193214495 x = -0.538193214495 Simplifying x = -0.538193214495Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.550538893505, -0.538193214495}
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