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Simplifying 3x2 + -42x + 145 = 0 Reorder the terms: 145 + -42x + 3x2 = 0 Solving 145 + -42x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 48.33333333 + -14x + x2 = 0 Move the constant term to the right: Add '-48.33333333' to each side of the equation. 48.33333333 + -14x + -48.33333333 + x2 = 0 + -48.33333333 Reorder the terms: 48.33333333 + -48.33333333 + -14x + x2 = 0 + -48.33333333 Combine like terms: 48.33333333 + -48.33333333 = 0.00000000 0.00000000 + -14x + x2 = 0 + -48.33333333 -14x + x2 = 0 + -48.33333333 Combine like terms: 0 + -48.33333333 = -48.33333333 -14x + x2 = -48.33333333 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -48.33333333 + 49 Reorder the terms: 49 + -14x + x2 = -48.33333333 + 49 Combine like terms: -48.33333333 + 49 = 0.66666667 49 + -14x + x2 = 0.66666667 Factor a perfect square on the left side: (x + -7)(x + -7) = 0.66666667 Calculate the square root of the right side: 0.816496583 Break this problem into two subproblems by setting (x + -7) equal to 0.816496583 and -0.816496583.Subproblem 1
x + -7 = 0.816496583 Simplifying x + -7 = 0.816496583 Reorder the terms: -7 + x = 0.816496583 Solving -7 + x = 0.816496583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 0.816496583 + 7 Combine like terms: -7 + 7 = 0 0 + x = 0.816496583 + 7 x = 0.816496583 + 7 Combine like terms: 0.816496583 + 7 = 7.816496583 x = 7.816496583 Simplifying x = 7.816496583Subproblem 2
x + -7 = -0.816496583 Simplifying x + -7 = -0.816496583 Reorder the terms: -7 + x = -0.816496583 Solving -7 + x = -0.816496583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -0.816496583 + 7 Combine like terms: -7 + 7 = 0 0 + x = -0.816496583 + 7 x = -0.816496583 + 7 Combine like terms: -0.816496583 + 7 = 6.183503417 x = 6.183503417 Simplifying x = 6.183503417Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.816496583, 6.183503417}
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