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Simplifying 3x(4x + 19) = 145 Reorder the terms: 3x(19 + 4x) = 145 (19 * 3x + 4x * 3x) = 145 (57x + 12x2) = 145 Solving 57x + 12x2 = 145 Solving for variable 'x'. Reorder the terms: -145 + 57x + 12x2 = 145 + -145 Combine like terms: 145 + -145 = 0 -145 + 57x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -12.08333333 + 4.75x + x2 = 0 Move the constant term to the right: Add '12.08333333' to each side of the equation. -12.08333333 + 4.75x + 12.08333333 + x2 = 0 + 12.08333333 Reorder the terms: -12.08333333 + 12.08333333 + 4.75x + x2 = 0 + 12.08333333 Combine like terms: -12.08333333 + 12.08333333 = 0.00000000 0.00000000 + 4.75x + x2 = 0 + 12.08333333 4.75x + x2 = 0 + 12.08333333 Combine like terms: 0 + 12.08333333 = 12.08333333 4.75x + x2 = 12.08333333 The x term is 4.75x. Take half its coefficient (2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. 4.75x + 5.640625 + x2 = 12.08333333 + 5.640625 Reorder the terms: 5.640625 + 4.75x + x2 = 12.08333333 + 5.640625 Combine like terms: 12.08333333 + 5.640625 = 17.72395833 5.640625 + 4.75x + x2 = 17.72395833 Factor a perfect square on the left side: (x + 2.375)(x + 2.375) = 17.72395833 Calculate the square root of the right side: 4.209983175 Break this problem into two subproblems by setting (x + 2.375) equal to 4.209983175 and -4.209983175.Subproblem 1
x + 2.375 = 4.209983175 Simplifying x + 2.375 = 4.209983175 Reorder the terms: 2.375 + x = 4.209983175 Solving 2.375 + x = 4.209983175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + x = 4.209983175 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = 4.209983175 + -2.375 x = 4.209983175 + -2.375 Combine like terms: 4.209983175 + -2.375 = 1.834983175 x = 1.834983175 Simplifying x = 1.834983175Subproblem 2
x + 2.375 = -4.209983175 Simplifying x + 2.375 = -4.209983175 Reorder the terms: 2.375 + x = -4.209983175 Solving 2.375 + x = -4.209983175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + x = -4.209983175 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = -4.209983175 + -2.375 x = -4.209983175 + -2.375 Combine like terms: -4.209983175 + -2.375 = -6.584983175 x = -6.584983175 Simplifying x = -6.584983175Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.834983175, -6.584983175}
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