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Simplifying 3x2 + -45x + 116 = 0 Reorder the terms: 116 + -45x + 3x2 = 0 Solving 116 + -45x + 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'. 38.66666667 + -15x + x2 = 0 Move the constant term to the right: Add '-38.66666667' to each side of the equation. 38.66666667 + -15x + -38.66666667 + x2 = 0 + -38.66666667 Reorder the terms: 38.66666667 + -38.66666667 + -15x + x2 = 0 + -38.66666667 Combine like terms: 38.66666667 + -38.66666667 = 0.00000000 0.00000000 + -15x + x2 = 0 + -38.66666667 -15x + x2 = 0 + -38.66666667 Combine like terms: 0 + -38.66666667 = -38.66666667 -15x + x2 = -38.66666667 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -38.66666667 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -38.66666667 + 56.25 Combine like terms: -38.66666667 + 56.25 = 17.58333333 56.25 + -15x + x2 = 17.58333333 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 17.58333333 Calculate the square root of the right side: 4.193248541 Break this problem into two subproblems by setting (x + -7.5) equal to 4.193248541 and -4.193248541.Subproblem 1
x + -7.5 = 4.193248541 Simplifying x + -7.5 = 4.193248541 Reorder the terms: -7.5 + x = 4.193248541 Solving -7.5 + x = 4.193248541 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 4.193248541 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 4.193248541 + 7.5 x = 4.193248541 + 7.5 Combine like terms: 4.193248541 + 7.5 = 11.693248541 x = 11.693248541 Simplifying x = 11.693248541Subproblem 2
x + -7.5 = -4.193248541 Simplifying x + -7.5 = -4.193248541 Reorder the terms: -7.5 + x = -4.193248541 Solving -7.5 + x = -4.193248541 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -4.193248541 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -4.193248541 + 7.5 x = -4.193248541 + 7.5 Combine like terms: -4.193248541 + 7.5 = 3.306751459 x = 3.306751459 Simplifying x = 3.306751459Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.693248541, 3.306751459}
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