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Simplifying x + 27x2 = 74 Solving x + 27x2 = 74 Solving for variable 'x'. Reorder the terms: -74 + x + 27x2 = 74 + -74 Combine like terms: 74 + -74 = 0 -74 + x + 27x2 = 0 Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. -2.740740741 + 0.03703703704x + x2 = 0 Move the constant term to the right: Add '2.740740741' to each side of the equation. -2.740740741 + 0.03703703704x + 2.740740741 + x2 = 0 + 2.740740741 Reorder the terms: -2.740740741 + 2.740740741 + 0.03703703704x + x2 = 0 + 2.740740741 Combine like terms: -2.740740741 + 2.740740741 = 0.000000000 0.000000000 + 0.03703703704x + x2 = 0 + 2.740740741 0.03703703704x + x2 = 0 + 2.740740741 Combine like terms: 0 + 2.740740741 = 2.740740741 0.03703703704x + x2 = 2.740740741 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.03703703704x + 0.25 + x2 = 2.740740741 + 0.25 Reorder the terms: 0.25 + 0.03703703704x + x2 = 2.740740741 + 0.25 Combine like terms: 2.740740741 + 0.25 = 2.990740741 0.25 + 0.03703703704x + x2 = 2.990740741 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.990740741 Calculate the square root of the right side: 1.729375824 Break this problem into two subproblems by setting (x + 0.5) equal to 1.729375824 and -1.729375824.Subproblem 1
x + 0.5 = 1.729375824 Simplifying x + 0.5 = 1.729375824 Reorder the terms: 0.5 + x = 1.729375824 Solving 0.5 + x = 1.729375824 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.729375824 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.729375824 + -0.5 x = 1.729375824 + -0.5 Combine like terms: 1.729375824 + -0.5 = 1.229375824 x = 1.229375824 Simplifying x = 1.229375824Subproblem 2
x + 0.5 = -1.729375824 Simplifying x + 0.5 = -1.729375824 Reorder the terms: 0.5 + x = -1.729375824 Solving 0.5 + x = -1.729375824 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.729375824 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.729375824 + -0.5 x = -1.729375824 + -0.5 Combine like terms: -1.729375824 + -0.5 = -2.229375824 x = -2.229375824 Simplifying x = -2.229375824Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.229375824, -2.229375824}
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