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Simplifying x(3x + 7) = 258 Reorder the terms: x(7 + 3x) = 258 (7 * x + 3x * x) = 258 (7x + 3x2) = 258 Solving 7x + 3x2 = 258 Solving for variable 'x'. Reorder the terms: -258 + 7x + 3x2 = 258 + -258 Combine like terms: 258 + -258 = 0 -258 + 7x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -86 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '86' to each side of the equation. -86 + 2.333333333x + 86 + x2 = 0 + 86 Reorder the terms: -86 + 86 + 2.333333333x + x2 = 0 + 86 Combine like terms: -86 + 86 = 0 0 + 2.333333333x + x2 = 0 + 86 2.333333333x + x2 = 0 + 86 Combine like terms: 0 + 86 = 86 2.333333333x + x2 = 86 The x term is 2.333333333x. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333x + 1.361111112 + x2 = 86 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = 86 + 1.361111112 Combine like terms: 86 + 1.361111112 = 87.361111112 1.361111112 + 2.333333333x + x2 = 87.361111112 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 87.361111112 Calculate the square root of the right side: 9.346716595 Break this problem into two subproblems by setting (x + 1.166666667) equal to 9.346716595 and -9.346716595.Subproblem 1
x + 1.166666667 = 9.346716595 Simplifying x + 1.166666667 = 9.346716595 Reorder the terms: 1.166666667 + x = 9.346716595 Solving 1.166666667 + x = 9.346716595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = 9.346716595 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 9.346716595 + -1.166666667 x = 9.346716595 + -1.166666667 Combine like terms: 9.346716595 + -1.166666667 = 8.180049928 x = 8.180049928 Simplifying x = 8.180049928Subproblem 2
x + 1.166666667 = -9.346716595 Simplifying x + 1.166666667 = -9.346716595 Reorder the terms: 1.166666667 + x = -9.346716595 Solving 1.166666667 + x = -9.346716595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = -9.346716595 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -9.346716595 + -1.166666667 x = -9.346716595 + -1.166666667 Combine like terms: -9.346716595 + -1.166666667 = -10.513383262 x = -10.513383262 Simplifying x = -10.513383262Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.180049928, -10.513383262}
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