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Simplifying 92x * 27(3 + -1x) = 0.11 Reorder the terms for easier multiplication: 92 * 27x(3 + -1x) = 0.11 Multiply 92 * 27 2484x(3 + -1x) = 0.11 (3 * 2484x + -1x * 2484x) = 0.11 (7452x + -2484x2) = 0.11 Solving 7452x + -2484x2 = 0.11 Solving for variable 'x'. Reorder the terms: -0.11 + 7452x + -2484x2 = 0.11 + -0.11 Combine like terms: 0.11 + -0.11 = 0.00 -0.11 + 7452x + -2484x2 = 0.00 Begin completing the square. Divide all terms by -2484 the coefficient of the squared term: Divide each side by '-2484'. 0.00004428341385 + -3x + x2 = 0.00 Move the constant term to the right: Add '-0.00004428341385' to each side of the equation. 0.00004428341385 + -3x + -0.00004428341385 + x2 = 0.00 + -0.00004428341385 Reorder the terms: 0.00004428341385 + -0.00004428341385 + -3x + x2 = 0.00 + -0.00004428341385 Combine like terms: 0.00004428341385 + -0.00004428341385 = 0.00000000000000 0.00000000000000 + -3x + x2 = 0.00 + -0.00004428341385 -3x + x2 = 0.00 + -0.00004428341385 Combine like terms: 0.00 + -0.00004428341385 = -0.00004428341385 -3x + x2 = -0.00004428341385 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -0.00004428341385 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -0.00004428341385 + 2.25 Combine like terms: -0.00004428341385 + 2.25 = 2.24995571658615 2.25 + -3x + x2 = 2.24995571658615 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 2.24995571658615 Calculate the square root of the right side: 1.499985239 Break this problem into two subproblems by setting (x + -1.5) equal to 1.499985239 and -1.499985239.Subproblem 1
x + -1.5 = 1.499985239 Simplifying x + -1.5 = 1.499985239 Reorder the terms: -1.5 + x = 1.499985239 Solving -1.5 + x = 1.499985239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.499985239 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.499985239 + 1.5 x = 1.499985239 + 1.5 Combine like terms: 1.499985239 + 1.5 = 2.999985239 x = 2.999985239 Simplifying x = 2.999985239Subproblem 2
x + -1.5 = -1.499985239 Simplifying x + -1.5 = -1.499985239 Reorder the terms: -1.5 + x = -1.499985239 Solving -1.5 + x = -1.499985239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.499985239 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.499985239 + 1.5 x = -1.499985239 + 1.5 Combine like terms: -1.499985239 + 1.5 = 0.000014761 x = 0.000014761 Simplifying x = 0.000014761Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.999985239, 0.000014761}
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