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Simplifying 174 = x(3x + 5) Reorder the terms: 174 = x(5 + 3x) 174 = (5 * x + 3x * x) 174 = (5x + 3x2) Solving 174 = 5x + 3x2 Solving for variable 'x'. Reorder the terms: 174 + -5x + -3x2 = 5x + -5x + 3x2 + -3x2 Combine like terms: 5x + -5x = 0 174 + -5x + -3x2 = 0 + 3x2 + -3x2 174 + -5x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 174 + -5x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -58 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '58' to each side of the equation. -58 + 1.666666667x + 58 + x2 = 0 + 58 Reorder the terms: -58 + 58 + 1.666666667x + x2 = 0 + 58 Combine like terms: -58 + 58 = 0 0 + 1.666666667x + x2 = 0 + 58 1.666666667x + x2 = 0 + 58 Combine like terms: 0 + 58 = 58 1.666666667x + x2 = 58 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 58 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 58 + 0.6944444447 Combine like terms: 58 + 0.6944444447 = 58.6944444447 0.6944444447 + 1.666666667x + x2 = 58.6944444447 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 58.6944444447 Calculate the square root of the right side: 7.661229956 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 7.661229956 and -7.661229956.Subproblem 1
x + 0.8333333335 = 7.661229956 Simplifying x + 0.8333333335 = 7.661229956 Reorder the terms: 0.8333333335 + x = 7.661229956 Solving 0.8333333335 + x = 7.661229956 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 7.661229956 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 7.661229956 + -0.8333333335 x = 7.661229956 + -0.8333333335 Combine like terms: 7.661229956 + -0.8333333335 = 6.8278966225 x = 6.8278966225 Simplifying x = 6.8278966225Subproblem 2
x + 0.8333333335 = -7.661229956 Simplifying x + 0.8333333335 = -7.661229956 Reorder the terms: 0.8333333335 + x = -7.661229956 Solving 0.8333333335 + x = -7.661229956 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -7.661229956 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -7.661229956 + -0.8333333335 x = -7.661229956 + -0.8333333335 Combine like terms: -7.661229956 + -0.8333333335 = -8.4945632895 x = -8.4945632895 Simplifying x = -8.4945632895Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.8278966225, -8.4945632895}
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