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Simplifying 3x2 + -32x + 75 = 0 Reorder the terms: 75 + -32x + 3x2 = 0 Solving 75 + -32x + 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'. 25 + -10.66666667x + x2 = 0 Move the constant term to the right: Add '-25' to each side of the equation. 25 + -10.66666667x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -10.66666667x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -10.66666667x + x2 = 0 + -25 -10.66666667x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -10.66666667x + x2 = -25 The x term is -10.66666667x. Take half its coefficient (-5.333333335). Square it (28.44444446) and add it to both sides. Add '28.44444446' to each side of the equation. -10.66666667x + 28.44444446 + x2 = -25 + 28.44444446 Reorder the terms: 28.44444446 + -10.66666667x + x2 = -25 + 28.44444446 Combine like terms: -25 + 28.44444446 = 3.44444446 28.44444446 + -10.66666667x + x2 = 3.44444446 Factor a perfect square on the left side: (x + -5.333333335)(x + -5.333333335) = 3.44444446 Calculate the square root of the right side: 1.855921458 Break this problem into two subproblems by setting (x + -5.333333335) equal to 1.855921458 and -1.855921458.Subproblem 1
x + -5.333333335 = 1.855921458 Simplifying x + -5.333333335 = 1.855921458 Reorder the terms: -5.333333335 + x = 1.855921458 Solving -5.333333335 + x = 1.855921458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.333333335' to each side of the equation. -5.333333335 + 5.333333335 + x = 1.855921458 + 5.333333335 Combine like terms: -5.333333335 + 5.333333335 = 0.000000000 0.000000000 + x = 1.855921458 + 5.333333335 x = 1.855921458 + 5.333333335 Combine like terms: 1.855921458 + 5.333333335 = 7.189254793 x = 7.189254793 Simplifying x = 7.189254793Subproblem 2
x + -5.333333335 = -1.855921458 Simplifying x + -5.333333335 = -1.855921458 Reorder the terms: -5.333333335 + x = -1.855921458 Solving -5.333333335 + x = -1.855921458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.333333335' to each side of the equation. -5.333333335 + 5.333333335 + x = -1.855921458 + 5.333333335 Combine like terms: -5.333333335 + 5.333333335 = 0.000000000 0.000000000 + x = -1.855921458 + 5.333333335 x = -1.855921458 + 5.333333335 Combine like terms: -1.855921458 + 5.333333335 = 3.477411877 x = 3.477411877 Simplifying x = 3.477411877Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.189254793, 3.477411877}
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