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Simplifying 3x2 + -152x + 3 = 0 Reorder the terms: 3 + -152x + 3x2 = 0 Solving 3 + -152x + 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'. 1 + -50.66666667x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -50.66666667x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -50.66666667x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -50.66666667x + x2 = 0 + -1 -50.66666667x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -50.66666667x + x2 = -1 The x term is -50.66666667x. Take half its coefficient (-25.33333334). Square it (641.7777781) and add it to both sides. Add '641.7777781' to each side of the equation. -50.66666667x + 641.7777781 + x2 = -1 + 641.7777781 Reorder the terms: 641.7777781 + -50.66666667x + x2 = -1 + 641.7777781 Combine like terms: -1 + 641.7777781 = 640.7777781 641.7777781 + -50.66666667x + x2 = 640.7777781 Factor a perfect square on the left side: (x + -25.33333334)(x + -25.33333334) = 640.7777781 Calculate the square root of the right side: 25.313588803 Break this problem into two subproblems by setting (x + -25.33333334) equal to 25.313588803 and -25.313588803.Subproblem 1
x + -25.33333334 = 25.313588803 Simplifying x + -25.33333334 = 25.313588803 Reorder the terms: -25.33333334 + x = 25.313588803 Solving -25.33333334 + x = 25.313588803 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25.33333334' to each side of the equation. -25.33333334 + 25.33333334 + x = 25.313588803 + 25.33333334 Combine like terms: -25.33333334 + 25.33333334 = 0.00000000 0.00000000 + x = 25.313588803 + 25.33333334 x = 25.313588803 + 25.33333334 Combine like terms: 25.313588803 + 25.33333334 = 50.646922143 x = 50.646922143 Simplifying x = 50.646922143Subproblem 2
x + -25.33333334 = -25.313588803 Simplifying x + -25.33333334 = -25.313588803 Reorder the terms: -25.33333334 + x = -25.313588803 Solving -25.33333334 + x = -25.313588803 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25.33333334' to each side of the equation. -25.33333334 + 25.33333334 + x = -25.313588803 + 25.33333334 Combine like terms: -25.33333334 + 25.33333334 = 0.00000000 0.00000000 + x = -25.313588803 + 25.33333334 x = -25.313588803 + 25.33333334 Combine like terms: -25.313588803 + 25.33333334 = 0.019744537 x = 0.019744537 Simplifying x = 0.019744537Solution
The solution to the problem is based on the solutions from the subproblems. x = {50.646922143, 0.019744537}
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