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Simplifying 3(x2 + x) = 71 Reorder the terms: 3(x + x2) = 71 (x * 3 + x2 * 3) = 71 (3x + 3x2) = 71 Solving 3x + 3x2 = 71 Solving for variable 'x'. Reorder the terms: -71 + 3x + 3x2 = 71 + -71 Combine like terms: 71 + -71 = 0 -71 + 3x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -23.66666667 + x + x2 = 0 Move the constant term to the right: Add '23.66666667' to each side of the equation. -23.66666667 + x + 23.66666667 + x2 = 0 + 23.66666667 Reorder the terms: -23.66666667 + 23.66666667 + x + x2 = 0 + 23.66666667 Combine like terms: -23.66666667 + 23.66666667 = 0.00000000 0.00000000 + x + x2 = 0 + 23.66666667 x + x2 = 0 + 23.66666667 Combine like terms: 0 + 23.66666667 = 23.66666667 x + x2 = 23.66666667 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. + 0.25 + x2 = 23.66666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 23.66666667 + 0.25 Combine like terms: 23.66666667 + 0.25 = 23.91666667 1.25 + x2 = 23.91666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 23.91666667 Calculate the square root of the right side: 4.890466917 Break this problem into two subproblems by setting (x + 0.5) equal to 4.890466917 and -4.890466917.Subproblem 1
x + 0.5 = 4.890466917 Simplifying x + 0.5 = 4.890466917 Reorder the terms: 0.5 + x = 4.890466917 Solving 0.5 + x = 4.890466917 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 = 4.890466917 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.890466917 + -0.5 x = 4.890466917 + -0.5 Combine like terms: 4.890466917 + -0.5 = 4.390466917 x = 4.390466917 Simplifying x = 4.390466917Subproblem 2
x + 0.5 = -4.890466917 Simplifying x + 0.5 = -4.890466917 Reorder the terms: 0.5 + x = -4.890466917 Solving 0.5 + x = -4.890466917 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 = -4.890466917 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.890466917 + -0.5 x = -4.890466917 + -0.5 Combine like terms: -4.890466917 + -0.5 = -5.390466917 x = -5.390466917 Simplifying x = -5.390466917Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.390466917, -5.390466917}
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