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Simplifying 2x2 + -15x + 23 = 0 Reorder the terms: 23 + -15x + 2x2 = 0 Solving 23 + -15x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 11.5 + -7.5x + x2 = 0 Move the constant term to the right: Add '-11.5' to each side of the equation. 11.5 + -7.5x + -11.5 + x2 = 0 + -11.5 Reorder the terms: 11.5 + -11.5 + -7.5x + x2 = 0 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + -7.5x + x2 = 0 + -11.5 -7.5x + x2 = 0 + -11.5 Combine like terms: 0 + -11.5 = -11.5 -7.5x + x2 = -11.5 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = -11.5 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = -11.5 + 14.0625 Combine like terms: -11.5 + 14.0625 = 2.5625 14.0625 + -7.5x + x2 = 2.5625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (x + -3.75) equal to 1.600781059 and -1.600781059.Subproblem 1
x + -3.75 = 1.600781059 Simplifying x + -3.75 = 1.600781059 Reorder the terms: -3.75 + x = 1.600781059 Solving -3.75 + x = 1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 1.600781059 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 1.600781059 + 3.75 x = 1.600781059 + 3.75 Combine like terms: 1.600781059 + 3.75 = 5.350781059 x = 5.350781059 Simplifying x = 5.350781059Subproblem 2
x + -3.75 = -1.600781059 Simplifying x + -3.75 = -1.600781059 Reorder the terms: -3.75 + x = -1.600781059 Solving -3.75 + x = -1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -1.600781059 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -1.600781059 + 3.75 x = -1.600781059 + 3.75 Combine like terms: -1.600781059 + 3.75 = 2.149218941 x = 2.149218941 Simplifying x = 2.149218941Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.350781059, 2.149218941}
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